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A072034
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Sum(binomial(n,k)*k^n,k=1..n).
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4
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1, 6, 54, 680, 11000, 217392, 5076400, 136761984, 4175432064, 142469423360, 5372711277824, 221903307604992, 9961821300640768, 482982946946734080, 25150966159083264000, 1400031335107317628928, 82960293298087664648192
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OFFSET
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1,2
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COMMENTS
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The number of functions from {1,2,...,n} into a subset of {1,2,...,n} summed over all subsets. - From Geoffrey Critzer, Sep 16 2012
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..200
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FORMULA
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E.g.f.: -LambertW(-x*exp(x))/(1+LambertW(-x*exp(x))). - Vladeta Jovovic, Mar 29 2008
a(n) ~ (n/(e*LambertW(1/e)))^n/sqrt(1+LambertW(1/e)). - Vaclav Kotesovec, Nov 26 2012
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MATHEMATICA
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Table[Sum[Binomial[n, k]k^n, {k, 1, n}], {n, 1, 20}] (* Geoffrey Critzer, Sep 16 2012 *)
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CROSSREFS
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Cf. A088789
Sequence in context: A034001 A084062 A137591 * A167571 A138434 A217238
Adjacent sequences: A072031 A072032 A072033 * A072035 A072036 A072037
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KEYWORD
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nonn,changed
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AUTHOR
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Karol A. Penson, Jun 07 2002
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STATUS
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approved
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