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A271702
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Triangle read by rows, T(n,k) = Sum_{j=0..n} (-1)^(n-j)*C(-j-1,-n-1)*S2(k,j), S2 the Stirling set numbers A048993, for n>=0 and 0<=k<=n.
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1
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1, 1, 1, 1, 2, 3, 1, 3, 6, 13, 1, 4, 10, 26, 71, 1, 5, 15, 45, 140, 456, 1, 6, 21, 71, 246, 887, 3337, 1, 7, 28, 105, 399, 1568, 6405, 27203, 1, 8, 36, 148, 610, 2584, 11334, 51564, 243203, 1, 9, 45, 201, 891, 4035, 18849, 91101, 455712, 2357356
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OFFSET
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0,5
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LINKS
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FORMULA
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EXAMPLE
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Triangle starts:
[1]
[1, 1]
[1, 2, 3]
[1, 3, 6, 13]
[1, 4, 10, 26, 71]
[1, 5, 15, 45, 140, 456]
[1, 6, 21, 71, 246, 887, 3337]
[1, 7, 28, 105, 399, 1568, 6405, 27203]
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MAPLE
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T := (n, k) -> add(Stirling2(k, j)*binomial(-j-1, -n-1)*(-1)^(n-j), j=0..n):
seq(seq(T(n, k), k=0..n), n=0..9);
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MATHEMATICA
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Flatten[Table[Sum[(-1)^(n-j) Binomial[-j-1, -n-1] StirlingS2[k, j], {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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