OFFSET
0,3
COMMENTS
This is the number of n X n square arrays with nonnegative integer entries in which every row and column add to 2 (A000681) normalized by dividing by n!/2^floor(n/2).
REFERENCES
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 125, #25, A_n.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
FORMULA
a(n) = A000681(n)*2^floor(n/2)/n!.
a(n) ~ 2^(floor(n/2) + 1/2) * n^n * exp(1/2-n). - Vaclav Kotesovec, Aug 13 2013
Recurrence: a(n) = (2*n^2 - 4*n + 1)*a(n-2) - (n-3)*n*a(n-4). - Vaclav Kotesovec, Aug 13 2013
MATHEMATICA
A000681[n_] := Sum[((2*i)!*n!^2)/(2^i*(i!^2*(n - i)!)), {i, 0, n}]/2^n;
a[n_] := A000681[n]*2^Floor[n/2]/n!;
Table[a[n], {n, 0, 19}]
(* Jean-François Alcover, Mar 14 2012, after Shanzhen Gao *)
CROSSREFS
KEYWORD
nonn,nice,easy
AUTHOR
EXTENSIONS
More terms from Vladeta Jovovic, Feb 11 2001
STATUS
approved