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A327751
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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.
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2
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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, 1200, 5646, 2160, 242, 0, 1, 0, 0, 8840, 101520, 121200, 16080, 728, 0, 1, 0, 70, 58800, 2103740, 6136800, 2410326, 115464, 2186, 0, 1
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OFFSET
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0,8
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COMMENTS
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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).
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LINKS
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FORMULA
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T(n,k) = Sum_{j=0..k} (-1)^(k-j) * binomial(k,j) * A002426(j)^n.
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EXAMPLE
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Square array begins:
1, 0, 0, 0, 0, 0, ...
1, 0, 2, 0, 6, 0, ...
1, 0, 8, 24, 216, 1200, ...
1, 0, 26, 264, 5646, 101520, ...
1, 0, 80, 2160, 121200, 6136800, ...
1, 0, 242, 16080, 2410326, 332810400, ...
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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