OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Zhanar Berikkyzy, Pamela E. Harris, Anna Pun, Catherine Yan, and Chenchen Zhao, Combinatorial Identities for Vacillating Tableaux, arXiv:2308.14183 [math.CO], 2023. See p. 24.
Wenyi Feng, "counting the number of matrix", sci.math article, Feb. 5, 1997.
Robert Israel, "Re: counting the number of matrix", sci.math article, Feb. 5, 1997.
Hyeong-Kwan Ju and Seunghyun Seo, Enumeration of 0/1-matrices avoiding some 2x2 matrices, arXiv:1107.1299 [math.CO], 2011.
Hyeong-Kwan Ju and Seunghyun Seo, Enumeration of (0,1)-matrices avoiding some 2 X 2 matrices, Discrete Math., 312 (2012), 2473-2481.
Susanna E. Rumsey, Stark C. Draper, and Frank R. Kschischang, Information Density in Multi-Layer Resistive Memories, IEEE Transactions on Information Theory (2020) Vol. 67, Issue 3, 1446-1460.
FORMULA
a(n) = Sum_{k=0..n} k! * Stirling2(n+1, k+1)^2.
EXAMPLE
For n = 2 the 12 matrices are all the 2 X 2 0-1 matrices except
[1 1] [1 0] [0 1] [1 1]
[1 0], [1 1], [1 1], [0 1]. - Robert Israel, Feb 19 2015
MAPLE
f:= n -> add(k!*combinat:-stirling2(n+1, k+1)^2, k = 0 .. n):
seq(f(n), n=0..30); # Robert Israel, Feb 19 2015
MATHEMATICA
Table[Sum[StirlingS2[n+1, k+1]^2k!, {k, 0, n}], {n, 0, 100}] (* Emanuele Munarini, Jul 04 2011 *)
PROG
(Maxima) makelist(sum(stirling2(n+1, k+1)^2*k!, k, 0, n), n, 0, 24); /* Emanuele Munarini, Jul 04 2011 */
(PARI) a(n) = sum(k=0, n, k! * stirling(n+1, k+1, 2)^2); \\ Michel Marcus, Feb 21 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
a(0)=1 added by Emanuele Munarini, Jul 04 2011
STATUS
approved