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A325146
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A(n, k) = Stirling2(n + k, k)*A053657(n)*k!/(n + k)!, array read by ascending antidiagonals for n >= 0 and k >= 0.
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0
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1, 0, 1, 0, 1, 1, 0, 4, 2, 1, 0, 2, 14, 3, 1, 0, 48, 12, 30, 4, 1, 0, 16, 496, 36, 52, 5, 1, 0, 576, 288, 2064, 80, 80, 6, 1, 0, 144, 18288, 1656, 5832, 150, 114, 7, 1, 0, 3840, 8160, 145200, 5920, 13240, 252, 154, 8, 1
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OFFSET
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0,8
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LINKS
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EXAMPLE
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[0] 1, 1, 1, 1, 1, 1, 1, 1, ... A000012
[1] 0, 1, 2, 3, 4, 5, 6, 7, ... A001477
[2] 0, 4, 14, 30, 52, 80, 114, 154, ... A049451
[3] 0, 2, 12, 36, 80, 150, 252, 392, ... A011379
[4] 0, 48, 496, 2064, 5832, 13240, 26088, 46536, ...
[5] 0, 16, 288, 1656, 5920, 16200, 37296, 76048, ...
[6] 0, 576, 18288, 145200, 654816, 2153280, 5775936, 13429248, ...
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MAPLE
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A := (n, k) -> Stirling2(n + k, k)*A053657(n)*k!/(n + k)!:
seq(seq(A(n - k, k), k=0..n), n=0..10);
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MATHEMATICA
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a053657[n_] := Product[p^Sum[Floor[(n-1) / ((p-1) p^k)], {k, 0, n}], {p, Prime[Range[n]]}];
A[n_, k_] := StirlingS2[n+k, k] a053657[n+1] k! / (n+k)!;
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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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