OFFSET
0,2
COMMENTS
Equals the self-convolution of A027826. Also equals antidiagonal sums of symmetric square array A100936. - Paul D. Hanna, Nov 22 2004
Equals eigensequence of triangle A152198. - Gary W. Adamson, Nov 28 2008
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
N. J. A. Sloane, Transforms
FORMULA
a(n) = 1 + Sum_{k=1..n} Sum_{j=0..n-k} C(k, j)*C(n-k, j)*a(j). - Paul D. Hanna, Nov 22 2004
G.f. A(x) satisfies: A(x) = A(x^2/(1-x)^2)/(1-x)^2 and A(x^2) = A(x/(1+x))/(1+x)^2. - Paul D. Hanna, Nov 22 2004
a(0) = 1; a(n) = Sum_{k=0..floor(n/2)} binomial(n+1,2*k+1) * a(k). - Ilya Gutkovskiy, Apr 07 2022
MAPLE
a:= proc(n) option remember; add(`if`(k<2, 1,
a(iquo(k, 2)))*binomial(n, k), k=0..n)
end:
seq(a(n), n=0..40); # Alois P. Heinz, Jul 08 2015
MATHEMATICA
a[n_] := a[n] = 1 + Sum[Binomial[k, j]*Binomial[n-k, j]*a[j], {k, 1, n}, {j, 0, n-k}]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Nov 11 2015 *)
PROG
(PARI) a(n)=1+sum(k=1, n, sum(j=0, n-k, binomial(k, j)*binomial(n-k, j)*a(j)))
(PARI) a(n)=local(A, m); if(n<0, 0, m=1; A=1+O(x); while(m<=n, m*=2; A=subst(A, x, (x/(1-x))^2)/(1-x)); polcoeff(A^2, n))
for(n=0, 40, print1(a(n), ", ")) \\ Paul D. Hanna, Nov 22 2004
CROSSREFS
KEYWORD
easy,nonn,eigen
AUTHOR
EXTENSIONS
More terms from Vladeta Jovovic, Jul 26 2002
STATUS
approved