The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A111146

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A111146

Triangle T(n,k), read by rows, given by [0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, ...] DELTA [1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, ...] where DELTA is the operator defined in A084938.
(history; published version)

#16 by N. J. A. Sloane at Sun May 26 14:55:03 EDT 2019

STATUS

proposed

approved

#15 by Jean-François Alcover at Sun May 26 13:19:56 EDT 2019

STATUS

editing

proposed

#14 by Jean-François Alcover at Sun May 26 13:19:50 EDT 2019

MATHEMATICA

T[n_, k_] := Module[{x = X + X*O[X]^n, y = Y + Y*O[Y]^k}, A = 1/(1 - x*y*Sum[x^j*Product[y + i, {i, 0, j - 1}], {j, 0, n}]); Coefficient[ Coefficient[A, X, n], Y, k]];

Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, May 26 2019, from PARI *)

STATUS

approved

editing

#13 by Alois P. Heinz at Sat Aug 08 11:15:10 EDT 2015

STATUS

editing

approved

#12 by Alois P. Heinz at Sat Aug 08 11:14:54 EDT 2015

LINKS

Alois P. Heinz, <a href="/A111146/b111146.txt">Rows n = 0..140, flattened</a>

STATUS

approved

editing

#11 by N. J. A. Sloane at Sun Sep 08 13:30:48 EDT 2013

AUTHOR

_Philippe DELEHAM_, Deléham_, Oct 19 2005

Discussion

Sun Sep 08

13:30

OEIS Server: https://oeis.org/edit/global/1938

#10 by Russ Cox at Sat Mar 31 10:27:52 EDT 2012

AUTHOR

_Philippe DELEHAM (kolotoko(AT)wanadoo.fr), _, Oct 19 2005

Discussion

Sat Mar 31

10:27

OEIS Server: https://oeis.org/edit/global/535

#9 by Russ Cox at Fri Mar 30 18:36:50 EDT 2012

FORMULA

G.f.: A(x, y) = 1/(1 - x*y*Sum_{j>=0} (y-1+j)!/(y-1)!*x^j ). - _Paul D. Hanna (pauldhanna(AT)juno.com), _, Oct 26 2005

Discussion

Fri Mar 30

18:36

OEIS Server: https://oeis.org/edit/global/213

#8 by N. J. A. Sloane at Tue Jun 01 03:00:00 EDT 2010

EXAMPLE

.1;

.0, 1;

.0, 0, 2;

.0, 0, 1, 4;

.0, 0, 2, 5, 8;

.0, 0, 6, 15, 17, 16;

.0, 0, 24, 62, 68, 49, 32;

.0, 0, 120, 322, 359, 243, 129, 64;

.0, 0, 720, 2004, 2308, 1553, 756, 321, 128;

.0, 0, 5040, 14508, 17332, 11903, 5622, 2151, 769, 256;

.0, 0, 40320, 119664, 148232, 105048, 49840, 18066, 5756, 1793, 512;

...................................................................

....................................................................

KEYWORD

easy,nonn,tabl,new

#7 by N. J. A. Sloane at Sun Jun 29 03:00:00 EDT 2008

EXAMPLE

Triangle begins :

KEYWORD

easy,nonn,tabl,new