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%I #63 Oct 30 2019 11:13:35
%S 1,0,1,0,0,1,0,2,0,1,0,0,8,0,1,0,6,24,26,0,1,0,0,216,264,80,0,1,0,20,
%T 1200,5646,2160,242,0,1,0,0,8840,101520,121200,16080,728,0,1,0,70,
%U 58800,2103740,6136800,2410326,115464,2186,0,1
%N Square array T(n,k), n>=0, k>=0, read by antidiagonals, where T(n,k) is the constant term in the expansion of (-1 + Product_{j=1..n} (1 + x_j + 1/x_j))^k.
%C T(n,k) is the number of k-step closed walks (from origin to origin) in n-dimensional lattice, using steps (t_1,t_2, ... ,t_n) (t_j = -1, 1 or 0 for 1 <= j <= n) except for (0,0, ... ,0) (t_j = 0 for 1 <= j <= n).
%H Seiichi Manyama, <a href="/A327751/b327751.txt">Antidiagonals n = 0..93, flattened</a>
%F T(n,k) = Sum_{j=0..k} (-1)^(k-j) * binomial(k,j) * A002426(j)^n.
%e Square array begins:
%e 1, 0, 0, 0, 0, 0, ...
%e 1, 0, 2, 0, 6, 0, ...
%e 1, 0, 8, 24, 216, 1200, ...
%e 1, 0, 26, 264, 5646, 101520, ...
%e 1, 0, 80, 2160, 121200, 6136800, ...
%e 1, 0, 242, 16080, 2410326, 332810400, ...
%Y Columns k=0-3 give A000012, A000004, A024023, 24*A016212(n-2).
%Y Rows n=0-4 give A000007, A126869, A094061, A328874, A328875.
%Y Main diagonal is A326920.
%Y Cf. A002426, A328718.
%K nonn,tabl
%O 0,8
%A _Seiichi Manyama_, Oct 30 2019
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