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A087650
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Sum_{k=0..n} (-1)^(n-k)*Bell(k).
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4
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1, 0, 2, 3, 12, 40, 163, 714, 3426, 17721, 98254, 580316, 3633281, 24011156, 166888166, 1216070379, 9264071768, 73600798036, 608476008123, 5224266196934, 46499892038438, 428369924118313, 4078345814329010, 40073660040755336
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..23.
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FORMULA
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E.g.f.: exp(-x)*((exp(x)-1)*exp(exp(x)-1)+1).
a(n)= (-1)^n + Bell(n) - A000296(n), with Bell(n)=A000110(n). Wolfdieter Lang, Dec 01 2003
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MATHEMATICA
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f[n_] := Sum[ StirlingS2[n, k], {k, 1, n}]; Table[(-1)^n + Sum[(-1)^(n - k)*f[k], {k, 0, n}], {n, 0, 23}] (from Robert G. Wilson v)
Needs["DiscreteMath`Combinatorica`"]; Table[ Sum[(-1)^(n - k)*BellB[k], {k, 0, n}], {n, 0, 23}] (from Robert G. Wilson v)
(Maxima) makelist(sum((-1)^(n-k)*belln(k), k, 0, n), n, 0, 40); [Emanuele Munarini, Sep 27 2012]
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CROSSREFS
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Cf. A000110, A000296, A005001, A005493.
Sequence in context: A012310 A082526 A151368 * A177699 A012514 A012511
Adjacent sequences: A087647 A087648 A087649 * A087651 A087652 A087653
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KEYWORD
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nonn,changed
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AUTHOR
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Vladeta Jovovic, Sep 23 2003
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STATUS
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approved
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