Search: seq:1,1,0 seq:-9 seq:-40,125,3444,18571 seq:-241872 seq:-5796711
(Hint: to search for an exact subsequence, use commas to separate the numbers.)
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A344053
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a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n, k)*Stirling2(n, k)*k!.
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+100
1
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1, 1, 0, -9, -40, 125, 3444, 18571, -241872, -5796711, -24387220, 1132278191, 25132445832, 8850583573, -10681029498972, -214099676807085, 1643397436986464, 176719161389104817, 2976468247699317468, -71662294521163070153, -4638920054290748840520, -55645074852328083377619
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OFFSET
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0,4
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COMMENTS
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Inverse binomial convolution of the Fubini numbers (A131689).
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LINKS
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FORMULA
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MATHEMATICA
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a[n_] := Sum[(-1)^(n - k) * Binomial[n, k] * StirlingS2[n, k] * k!, {k, 0, n}]; Array[a, 22, 0] (* Amiram Eldar, May 10 2021 *)
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PROG
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(PARI) a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n, k)*stirling(n, k, 2)*k!); \\ Michel Marcus, May 10 2021
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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