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A336187
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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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3
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1, 1, 1, 1, 2, 1, 1, 3, 4, 1, 1, 4, 13, 8, 1, 1, 5, 34, 63, 16, 1, 1, 6, 81, 352, 321, 32, 1, 1, 7, 186, 1685, 3946, 1683, 64, 1, 1, 8, 421, 7416, 38401, 46744, 8989, 128, 1, 1, 9, 946, 30835, 328146, 963525, 573616, 48639, 256, 1, 1, 10, 2113, 122816, 2590225, 16971876, 25346385, 7217536, 265729, 512, 1
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OFFSET
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0,5
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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, 2, 3, 4, 5, 6, ...
1, 4, 13, 34, 81, 186, ...
1, 8, 63, 352, 1685, 7416, ...
1, 16, 321, 3946, 38401, 328146, ...
1, 32, 1683, 46744, 963525, 16971876, ...
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MATHEMATICA
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Unprotect[Power]; 0^0 = 1; T[n_, k_] := Sum[ k^j*Binomial[n, j]^k, {j, 0, n}]; Table[T[k, n - k], {n, 0, 10}, {k, 0, n}] // Flatten (* Amiram Eldar, Jul 11 2020 *)
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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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