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%I M2704 #31 Oct 03 2017 01:31:23
%S 1,1,3,7,47,207,2249,14501,216273,1830449,34662523,362983263,
%T 8330310559,103938238111,2801976629841,40574514114061,
%U 1256354802202337,20708839411614753,724160187180691379,13386284447024070647
%N Number of "magic squares" of order n (see comment line for exact definition).
%C 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).
%D L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 125, #25, A_n.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Vincenzo Librandi, <a href="/A005650/b005650.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Mag#magic">Index entries for sequences related to magic squares</a>
%F a(n) = A000681(n)*2^floor(n/2)/n!.
%F a(n) ~ 2^(floor(n/2) + 1/2) * n^n * exp(1/2-n). - _Vaclav Kotesovec_, Aug 13 2013
%F Recurrence: a(n) = (2*n^2 - 4*n + 1)*a(n-2) - (n-3)*n*a(n-4). - _Vaclav Kotesovec_, Aug 13 2013
%t A000681[n_] := Sum[((2*i)!*n!^2)/(2^i*(i!^2*(n - i)!)), {i, 0, n}]/2^n;
%t a[n_] := A000681[n]*2^Floor[n/2]/n!;
%t Table[a[n], {n, 0, 19}]
%t (* _Jean-François Alcover_, Mar 14 2012, after _Shanzhen Gao_ *)
%K nonn,nice,easy
%O 0,3
%A _N. J. A. Sloane_, _Simon Plouffe_
%E More terms from _Vladeta Jovovic_, Feb 11 2001
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