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A336201
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Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) = Sum_{j=0..n} (-k)^j * binomial(n,j)^k.
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1
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1, 1, 1, 1, 0, 1, 1, -1, 0, 1, 1, -2, -3, 0, 1, 1, -3, -14, 11, 0, 1, 1, -4, -47, 136, 1, 0, 1, 1, -5, -134, 909, 106, -81, 0, 1, 1, -6, -347, 4736, 3585, -8492, 141, 0, 1, 1, -7, -846, 21655, 61906, -323523, 35344, 363, 0, 1, 1, -8, -1983, 91512, 771601, -8065624, 2201809, 395008, -1791, 0, 1
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OFFSET
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0,12
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COMMENTS
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Column k is the diagonal of the rational function 1 / (Product_{j=1..k} (1-x_j) + k * Product_{j=1..k} x_j) for k>0.
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LINKS
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EXAMPLE
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Square array begins:
1, 1, 1, 1, 1, 1, ...
1, 0, -1, -2, -3, -4, ...
1, 0, -3, -14, -47, -134, ...
1, 0, 11, 136, 909, 4736, ...
1, 0, 1, 106, 3585, 61906, ...
1, 0, -81, -8492, -323523, -8065624, ...
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MATHEMATICA
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T[n_, k_] := Sum[If[k == j == 0, 1, (-k)^j] * Binomial[n, j]^k, {j, 0, n}]; Table[T[k, n-k], {n, 0, 10}, {k, 0, n}] // Flatten (* Amiram Eldar, May 01 2021 *)
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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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