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A269954
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Triangle read by rows, T(n,k) = Sum_{j=0..n} C(-j,-n)*S1(j,k), S1 the Stirling cycle numbers A132393, for n>=0 and 0<=k<=n.
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1
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1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 2, 5, 3, 1, 0, 9, 20, 17, 6, 1, 0, 44, 109, 100, 45, 10, 1, 0, 265, 689, 694, 355, 100, 15, 1, 0, 1854, 5053, 5453, 3094, 1015, 196, 21, 1, 0, 14833, 42048, 48082, 29596, 10899, 2492, 350, 28, 1
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OFFSET
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0,12
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LINKS
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EXAMPLE
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Triangle starts:
1,
0, 1,
0, 0, 1,
0, 1, 1, 1,
0, 2, 5, 3, 1,
0, 9, 20, 17, 6, 1,
0, 44, 109, 100, 45, 10, 1,
0, 265, 689, 694, 355, 100, 15, 1.
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MAPLE
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A269954 := (n, k) -> add(binomial(-j, -n)*abs(Stirling1(j, k)), j=0..n):
seq(seq(A269954(n, k), k=0..n), n=0..9);
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MATHEMATICA
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Flatten[Table[Sum[Binomial[-j, -n] Abs[StirlingS1[j, k]], {j, 0, n}], {n, 0, 9}, {k, 0, n}]]
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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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