login
The OEIS is supported by the many generous donors to the OEIS Foundation.
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
Search: a112940 -id:a112940
Displaying 1-9 of 9 results found.
page 1
     Sort: relevance | references | number | modified | created      Format: long | short | data
A112941
Logarithmic derivative of A112940 such that a(n)=(1/5)*A112940(n+1) for n>0, where A112940 equals the INVERT transform (with offset) of quintuple factorials A008546.
+20
9
1, 9, 121, 2209, 51401, 1457649, 48774041, 1880312129, 82028211241, 3993290362449, 214543742998201, 12606663551853409, 804145149477634121, 55332318403485181809, 4084986234723143402201, 322064057582671115832449
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Table of n, a(n) for n=1..16.
FORMULA
G.f.: log(1+x + 5*x*[Sum_{n>=1} a(n)]) = Sum_{n>=1} a(n)/n*x^n.
EXAMPLE
log(1+x + 5*x*[x + 9*x^2 + 121*x^3 + 2209*x^4 + 51401*x^5 +...])
= x + 9/2*x^2 + 121/3*x^3 + 2209/4*x^4 + 51401/5*x^5 + ...
PROG
(PARI) {a(n)=local(F=1+x+x*O(x^n)); for(i=1, n, F=1+x+5*x^2*deriv(F)/F); return(n*polcoeff(log(F), n, x))}
CROSSREFS
Cf. A008546, A112940; A112934, A112935, A112936, A112937, A112938, A112939, A112942, A112943.
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 09 2005
STATUS
approved
A112934
a(0) = 1; a(n+1) = Sum_{k=0..n} a(k)*A001147(n-k), where A001147 = double factorial numbers.
+10
26
1, 1, 2, 6, 26, 158, 1282, 13158, 163354, 2374078, 39456386, 737125446, 15279024026, 347786765150, 8621313613954, 231139787526822, 6663177374810266, 205503866668090750, 6751565903597571842
(list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
INVERT transform of double factorials (A001147), shifted right one place, where g.f. A(x) satisfies: A(x) = 1 + x*[d/dx x*A(x)^2]/A(x)^2.
G.f. A(x) satisfies: A(x) = 1+x + 2*x^2*[d/dx A(x)]/A(x) (log derivative).
G.f.: A(x) = 1+x +2*x^2/(1-3*x -2*2*1*x^2/(1-7*x -2*3*3*x^2/(1-11*x -2*4*5*x^2/(1-15*x - ... -2*n*(2*n-3)*x^2/(1-(4*n-1)*x - ...)))) (continued fraction).
G.f.: A(x) = 1/(1-x/(1 -1*x/(1-2*x/(1 -3*x/(1-4*x(1 - ...))))))) (continued fraction).
From Paul Barry, Dec 04 2009: (Start)
The g.f. of a(n+1) is 1/(1-2x/(1-x/(1-4x/(1-3x/(1-6x/(1-5x/(1-.... (continued fraction).
The Hankel transform of a(n+1) is A137592. (End)
a(n) = Sum_{k=0..n} A111106(n,k). - Philippe Deléham, Jun 20 2006
From Gary W. Adamson, Jul 08 2011: (Start)
a(n) is the upper left term in M^n, M = the production matrix:
1, 1;
1, 1, 2;
1, 1, 2, 3;
1, 1, 2, 3, 4;
1, 1, 2, 3, 4, 5;
... (End)
From Gary W. Adamson, Jul 21 2016: (Start)
Another production matrix Q is:
1, 1, 0, 0, 0, ...
1, 0, 3, 0, 0, ...
1, 0, 0, 5, 0, ...
1, 0, 0, 0, 7, ...
...
The sequence is generated by extracting the upper left term of powers of Q. By extracting the top row of Q^n, we obtain a triangle with the sequence in the left column and row sums = (1, 2, 6, 26, 158, ...): (1), (1, 1), (2, 1, 3), (6, 2, 3, 15), (26, 6, 6, 15, 105), ... (End)
a(n) = (2*n - 1) * a(n-1) - Sum_{k=1..n-1} a(k) * a(n-k) if n>1. - Michael Somos, Jul 23 2011
G.f.: 1 / (1 - b(0)*x / (1 - b(1)*x / ...)) where b = A028310. - Michael Somos, Mar 31 2012
From Sergei N. Gladkovskii, Aug 11 2012, Aug 12 2012, Dec 26 2012, Mar 20 2013, Jun 02 2013, Aug 14 2013, Oct 22 2013: (Start) Continued fractions:
G.f. 1/(G(0)-x) where G(k) = 1 - x*(k+1)/G(k+1).
G.f. 1 + x/(G(0)-x) where G(k) = 1 - x*(k+1)/G(k+1).
G.f.: A(x) = 1 + x/(G(0) - x) where G(k) = 1 + (2*k+1)*x - x*(2*k+2)/G(k+1).
G.f.: Q(0) where Q(k) = 1 - x*(2*k-1)/(1 - x*(2*k+2)/Q(k+1)).
G.f.: 2/G(0) where G(k) = 1 + 1/(1 - x/(x + 1/(2*k-1)/G(k+1))).
G.f.: 3*x - G(0) where G(k) = 3*x - 2*x*k - 1 - x*(2*k-1)/G(k+1).
G.f.: 1 + x*Q(0) where Q(k) = 1 - x*(2*k+2)/(x*(2*k+2) - 1/(1 - x*(2*k+1)/(x*(2*k+1) - 1/Q(k+1)))). (End)
a(n) ~ n^(n-1) * 2^(n-1/2) / exp(n). - Vaclav Kotesovec, Feb 22 2014
EXAMPLE
A(x) = 1 + x + 2*x^2 + 6*x^3 + 26*x^4 + 158*x^5 + 1282*x^6 + ...
1/A(x) = 1 - x - x^2 - 3*x^3 - 15*x^4 - 105*x^5 - ... - A001147(n)*x^(n+1) - ...
a(4) = a(3+1) = Sum_{k=0..3} a(k)*A001147(3-k) = a(0)*5!! + a(1)*3!! + a(2)*1 + a(3)*1 = 1*15 + 1*3 + 2*1 + 6*1 = 26. - Michael B. Porter, Jul 22 2016
MAPLE
a_list := proc(len) local A, n; A[0] := 1; A[1] := 1;
for n from 2 to len-1 do A[n] := (2*n-1)*A[n-1] - add(A[j]*A[n-j], j=1..n-1) od;
convert(A, list) end: a_list(19); # Peter Luschny, May 22 2017
# Alternative:
T := proc(n, k) option remember; if k = 0 then 1 else if k = n then T(n, k-1)
else (n - k) * T(n, k - 1) + T(n - 1, k) fi fi end:
a := n -> T(n, n): seq(a(n), n = 0..18); # Peter Luschny, Oct 02 2023
MATHEMATICA
a[0] = 1; a[n_] := a[n] = Sum[a[k]*(2n - 2k - 3)!!, {k, 0, n - 1}]; Table[ a[n], {n, 0, 19}] (* Robert G. Wilson v, Oct 12 2005 *)
PROG
(PARI) {a(n)=local(F=1+x+x*O(x^n)); for(i=1, n, F=1+x+2*x^2*deriv(F)/F); return(polcoeff(F, n, x))}
(PARI) {a(n) = local(A); if( n<1, n==0, A = vector(n); A[1] = 1; for( k=2, n, A[k] = (2*k - 1) * A[k-1] - sum( j=1, k-1, A[j] * A[k-j])); A[n])} /* Michael Somos, Jul 23 2011 */
CROSSREFS
Cf. A001147, A112935 (log derivative); A112936, A112937, A112938, A112939, A112940, A112941, A112942, A112943.
KEYWORD
nonn
AUTHOR
Philippe Deléham and Paul D. Hanna, Oct 09 2005
STATUS
approved
A112936
INVERT transform (with offset) of triple factorials (A008544), where g.f. satisfies: A(x) = 1 + x*[d/dx x*A(x)^3]/A(x)^3.
+10
16
1, 1, 3, 15, 111, 1131, 14943, 243915, 4742391, 106912131, 2739347103, 78569371275, 2492748594471, 86650852740531, 3274367635513263, 133625238021647835, 5856377114106629751, 274320168321004350531
(list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
Table of n, a(n) for n=0..17.
FORMULA
G.f. satisfies: A(x) = 1+x + 3*x^2*[d/dx A(x)]/A(x) (log derivative).
G.f.: A(x) = 1+x +3*x^2/(1-5*x -3*2*2*x^2/(1-11*x -3*3*5*x^2/(1-17*x -3*4*8*x^2/(1-23*x -... -3*n*(3*n-4)*x^2/(1-(6*n-1)*x -...)))) (continued fraction).
G.f.: A(x) = 1/(1-x/(1 -2*x/(1-3*x/(1 -5*x/(1-6*x/(1 -8*x/(1-9*x/(1 -...)))))))) (continued fraction).
a(n) = (3*n - 2) * a(n-1) - Sum_{k=1..n-1} a(k) * a(n-k) if n>1. - Michael Somos, Jul 23 2011
G.f.: Q(0) where Q(k) = 1 - x*(3*k-1)/(1 - x*(3*k+3)/Q(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Mar 20 2013
G.f.: 2/G(0)+4*x, where G(k)= 1 + 1/(1 - x*(3*k+3)/(x*(3*k+5) + 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, May 25 2013
G.f.: 2/G(0), where G(k)= 1 + 1/(1 - x*(3*k-1)/(x*(3*k-1) + 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 06 2013
G.f.: -4/Sum_{n>=0} [Product_{k=0..n} (3*k-4)]*x^n. - Sergei N. Gladkovskii, Jun 06 2013
a(n) ~ n! * 3^(n-1) / (GAMMA(2/3) * n^(4/3)) . - Vaclav Kotesovec, Feb 22 2014
Given g.f. A(x), then y = x * A(x^3) satisfies y^2 = x*y + x^5*y'. - Michael Somos, Oct 17 2016
EXAMPLE
A(x) = 1 + x + 3*x^2 + 15*x^3 + 111*x^4 + 1131*x^5 + 14943*x^6 +...
1/A(x) = 1 - x - 2*x^2 - 10*x^3 - 80*x^4 - 880*x^5 -...-A008544(n)*x^(n+1)-...
MATHEMATICA
a = ConstantArray[0, 20]; a[[1]]=1; Do[a[[n]] = (3*n-2)*a[[n-1]] - Sum[a[[k]]*a[[n-k]], {k, 1, n-1}], {n, 2, 20}]; Flatten[{1, a}] (* Vaclav Kotesovec after Michael Somos, Feb 22 2014 *)
CoefficientList[Series[1/(1+(1/3*ExpIntegralE[2/3, -1/(3*x)])/E^(1/(3*x))), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 22 2014 *)
PROG
(PARI) {a(n)=local(F=1+x+x*O(x^n)); for(i=1, n, F=1+x+3*x^2*deriv(F)/F); return(polcoeff(F, n, x))}
(PARI) {a(n) = my(A); if( n<1, n==0, A = vector(n, k, 1); for(k=2, n, A[k] = (3*k - 2)*A[k-1] - sum(j=1, k-1, A[j] * A[k-j])); A[n])}; /* Michael Somos, Jul 23 2011 */
(PARI) {a(n) = if( n<1, n==0, polcoeff( 1 / sum(k=0, n, x^k * prod(i=1, k, 3*i - 4), x * O(x^n)), n))}; /* Michael Somos, Oct 17 2016 */
(PARI) {a(n) = my(A); if( n<0, 0, A = O(x); for(k=0, n, A = (x + sqrt(x^2 + 4*x^5*A')) / 2); polcoeff(A, 3*n + 1))}; /* Michael Somos, Oct 17 2016 */
(PARI) {a(n) = my(A); if( n<1, n==0, A = x; for(k=1, n, A = truncate(A) + O(x^(3*k + 4)); A += A + x^4*A' - A^2/x); polcoeff(A, 3*n + 1))}; /* Michael Somos, Oct 17 2016 */
CROSSREFS
Cf. A008544, A112937 (log derivative); A112934, A112935, A112938, A112939, A112940, A112941, A112942, A112943.
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 09 2005
STATUS
approved
A112938
INVERT transform (with offset) of quadruple factorials (A008545), where g.f. satisfies: A(x) = 1 + x*[d/dx x*A(x)^4]/A(x)^4.
+10
12
1, 1, 4, 28, 292, 4156, 75844, 1694812, 44835172, 1369657468, 47422855300, 1834403141788, 78377228106148, 3664969183404220, 186134931067171012, 10201887125268108508, 600142156513333537252, 37713563573426417361148
(list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
G.f. satisfies: A(x) = 1+x + 4*x^2*[d/dx A(x)]/A(x) (log derivative).
G.f.: A(x) = 1+x +4*x^2/(1-7*x -4*2*3*x^2/(1-15*x -4*3*7*x^2/(1-23*x -4*4*11*x^2/(1-31*x -... -4*n*(4*n-5)*x^2/(1-(8*n-1)*x -...)))) (continued fraction).
G.f.: A(x) = 1/(1-1*x/(1 -3*x/(1-4*x/(1 -7*x/(1-8*x/(1 -11*x/(1-12*x/(1 -...)))))))) (continued fraction).
G.f.: Q(0) where Q(k) = 1 - x*(4*k-1)/(1 - x*(4*k+4)/Q(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Mar 20 2013
G.f.: 1 + 2*x/G(0), where G(k)= 1 + 1/(1 - 2*x*(4*k+4)/(2*x*(4*k+4) - 1 + 2*x*(4*k+3)/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, May 31 2013
a(n) ~ (n-1)! * 4^(n-1) / (GAMMA(3/4) * n^(1/4)). - Vaclav Kotesovec, Feb 22 2014
EXAMPLE
A(x) = 1 + x + 4*x^2 + 28*x^3 + 292*x^4 + 4156*x^5 + ...
1/A(x) = 1 - x - 3*x^2 - 21*x^3 - 231*x^4 -... -A008545(n)*x^(n+1)-...
MATHEMATICA
CoefficientList[Series[1/(1 + 1/4*ExpIntegralE[3/4, -1/(4*x)]/E^(1/(4*x))), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 22 2014 *)
PROG
(PARI) {a(n)=local(F=1+x+x*O(x^n)); for(i=1, n, F=1+x+4*x^2*deriv(F)/F); return(polcoeff(F, n, x))}
CROSSREFS
Cf. A008545, A112939 (log derivative); A112934, A112935, A112936, A112937, A112940, A112941, A112942, A112943.
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 09 2005
STATUS
approved
A112942
INVERT transform (with offset) of sextuple factorials (A008543), where g.f. satisfies: A(x) = 1 + x*[d/dx x*A(x)^6]/A(x)^6.
+10
10
1, 1, 6, 66, 1086, 24186, 684006, 23506626, 951191646, 44281107066, 2330310876486, 136747268000706, 8851092668419326, 626304664252772346, 48092138192079689766, 3982448437177141451586, 353746119265020213643806
(list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Generally, if g.f. satisfies: A(x) = 1 + x*[d/dx x*A(x)^p]/A(x)^p, then a(n) ~ (n-1)! * p^(n-1) / (Gamma((p-1)/p) * n^(1/p)). - Vaclav Kotesovec, Feb 22 2014
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
G.f. satisfies: A(x) = 1+x + 6*x^2*[d/dx A(x)]/A(x) (log derivative).
G.f.: A(x) = 1+x+6*x^2/(1-11*x-6*2*5*x^2/(1-23*x-6*3*11*x^2/(1-35*x -6*4*17*x^2/(1-47*x- ... -6*n*(6*n-7)*x^2/(1-(12*n-1)*x - ...)))) (continued fraction).
G.f.: A(x) = 1/(1-1*x/(1-5*x/(1-6*x/(1-11*x/(1-12*x/(1-17*x/(1-18*x/(1 -...)))))))) (continued fraction).
G.f.: G(0) where G(k) = 1 - x*(6*k-1)/( 1 - 6*x*(k+1)/G(k+1) ); (continued fraction ). - Sergei N. Gladkovskii, Mar 24 2013
a(n) ~ (n-1)! * 6^(n-1) / (Gamma(5/6) * n^(1/6)). - Vaclav Kotesovec, Feb 22 2014
EXAMPLE
A(x) = 1 + x + 6*x^2 + 66*x^3 + 1086*x^4 + 24186*x^5 +...
1/A(x) = 1 - x - 5*x^2 - 55*x^3 - 935*x^4 -... -A008543(n)*x^(n+1)-...
MATHEMATICA
CoefficientList[Series[1/(1 + 1/6*ExpIntegralE[5/6, -1/(6*x)]/E^(1/(6*x))), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 22 2014 *)
PROG
(PARI) {a(n)=local(F=1+x+x*O(x^n)); for(i=1, n, F=1+x+6*x^2*deriv(F)/F); return(polcoeff(F, n, x))}
CROSSREFS
Cf. A008543, A112943 (log derivative); A112934, A112935, A112936, A112937, A112938, A112939, A112940, A112941.
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 09 2005
STATUS
approved
A112935
Logarithmic derivative of A112934 such that a(n)=(1/2)*A112934(n+1) for n>0, where A112934 equals the INVERT transform of double factorials A001147.
+10
9
1, 3, 13, 79, 641, 6579, 81677, 1187039, 19728193, 368562723, 7639512013, 173893382575, 4310656806977, 115569893763411, 3331588687405133, 102751933334045375, 3375782951798785921, 117693183724386637635
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Table of n, a(n) for n=1..18.
FORMULA
G.f.: log(1 + x + 2*x*[Sum_{n>=1} a(n)*x^n]) = Sum_{k>=1} a(n)/n*x^n.
G.f.: (1 - 1/Q(0))/x where Q(k) = 1 - x*(2*k-1)/(1 - x*(2*k+4)/Q(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Mar 19 2013
G.f.: 1/(x*G(0)) - 1/(2*x), where G(k)= 1 + 1/(1 - 2*x*(2*k+2)/(2*x*(2*k+2) - 1 + 2*x*(2*k+1)/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, May 31 2013
EXAMPLE
log(1+x + 2*x*[x + 3*x^2 + 13*x^3 + 79*x^4 + 641*x^5 +...])
= x + 3/2*x^2 + 13/3*x^3 + 79/4*x^4 + 641/5*x^5 +...
PROG
(PARI) {a(n)=local(F=1+x+x*O(x^n)); for(i=1, n, F=1+x+2*x^2*deriv(F)/F); return(n*polcoeff(log(F), n, x))}
CROSSREFS
Cf. A001147, A112934; A112936, A112937, A112938, A112939, A112940, A112941, A112942, A112943.
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 09 2005
STATUS
approved
A112937
Logarithmic derivative of A112936 such that a(n)=(1/3)*A112936(n+1) for n>0, where A112936 equals the INVERT transform (with offset) of triple factorials A008544.
+10
9
1, 5, 37, 377, 4981, 81305, 1580797, 35637377, 913115701, 26189790425, 830916198157, 28883617580177, 1091455878504421, 44541746007215945, 1952125704702209917, 91440056107001450177, 4558596081095404198741
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Table of n, a(n) for n=1..17.
FORMULA
G.f.: log(1+x + 3*x*[Sum_{k>=1} a(n)]) = Sum_{k>=1} a(n)/n*x^n.
EXAMPLE
log(1+x + 3*x*[x + 5*x^2 + 37*x^3 + 377*x^4 + 4981*x^5 +...])
= x + 5/2*x^2 + 37/3*x^3 + 377/4*x^4 + 4981/5*x^5 + ...
PROG
(PARI) {a(n)=local(F=1+x+x*O(x^n)); for(i=1, n, F=1+x+3*x^2*deriv(F)/F); return(n*polcoeff(log(F), n, x))}
CROSSREFS
Cf. A008544, A112936; A112934, A112935, A112938, A112939, A112940, A112941, A112942, A112943.
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 09 2005
STATUS
approved
A112939
Logarithmic derivative of A112938 such that a(n)=(1/4)*A112938(n+1) for n>0, where A112938 equals the INVERT transform (with offset) of quadruple factorials A008545.
+10
9
1, 7, 73, 1039, 18961, 423703, 11208793, 342414367, 11855713825, 458600785447, 19594307026537, 916242295851055, 46533732766792753, 2550471781317027127, 150035539128333384313, 9428390893356604340287, 630318228814408172573761
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Table of n, a(n) for n=1..17.
FORMULA
G.f.: log(1+x + 4*x*[Sum_{k>=1} a(n)]) = Sum_{k>=1} a(n)/n*x^n.
G.f.: 1/x - G(0)/(2*x), where G(k)= 1 + 1/(1 - x*(4*k-1)/(x*(4*k-3) + 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 04 2013
EXAMPLE
log(1+x + 4*x*[x + 7*x^2 + 73*x^3 + 1039*x^4 + 18961*x^5 +...])
= x + 7/2*x^2 + 73/3*x^3 + 1039/4*x^4 + 18961/5*x^5 + ...
PROG
(PARI) {a(n)=local(F=1+x+x*O(x^n)); for(i=1, n, F=1+x+4*x^2*deriv(F)/F); return(n*polcoeff(log(F), n, x))}
CROSSREFS
Cf. A008545, A112938; A112934, A112935, A112936, A112937, A112940, A112941, A112942, A112943.
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 09 2005
STATUS
approved
A112943
Logarithmic derivative of A112942 such that a(n)=(1/6)*A112942(n+1) for n>0, where A112942 equals the INVERT transform (with offset) of sextuple factorials A008543.
+10
9
1, 11, 181, 4031, 114001, 3917771, 158531941, 7380184511, 388385146081, 22791211333451, 1475182111403221, 104384110708795391, 8015356365346614961, 663741406196190241931, 58957686544170035607301
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Table of n, a(n) for n=1..15.
FORMULA
G.f.: log(1+x + 6*x*[Sum_{n>=1} a(n)]) = Sum_{n>=1} a(n)/n*x^n.
EXAMPLE
log(1+x + 6*x*[x + 11*x^2 + 181*x^3 + 4031*x^4 + 114001*x^5 +...])
= x + 11/2*x^2 + 181/3*x^3 + 4031/4*x^4 + 114001/5*x^5 + ...
PROG
(PARI) {a(n)=local(F=1+x+x*O(x^n)); for(i=1, n, F=1+x+6*x^2*deriv(F)/F); return(n*polcoeff(log(F), n, x))}
CROSSREFS
Cf. A008543, A112942; A112934, A112935, A112936, A112937, A112938, A112939, A112940, A112941.
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 09 2005
STATUS
approved
page 1

Search completed in 0.006 seconds

Lookup Welcome Wiki Register Music Plot 2 Demos Index WebCam Contribute Format Style Sheet Transforms Superseeker Recents
The OEIS Community
Maintained by The OEIS Foundation Inc.
Last modified March 12 12:34 EDT 2025. Contains 381711 sequences.
License Agreements, Terms of Use, Privacy Policy