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A072034
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a(n) = Sum_{k=0..n} binomial(n,k)*k^n.
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36
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1, 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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0,3
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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. - Geoffrey Critzer, Sep 16 2012
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LINKS
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FORMULA
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a(n) ~ (n/(e*LambertW(1/e)))^n/sqrt(1+LambertW(1/e)). - Vaclav Kotesovec, Nov 26 2012
O.g.f.: Sum_{n>=0} n^n * x^n / (1 - n*x)^(n+1). - Paul D. Hanna, May 22 2018
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MAPLE
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seq(add(binomial(n, k)*k^n, k=0..n), n=0..17); # Peter Luschny, Jun 09 2015
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MATHEMATICA
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Table[Sum[Binomial[n, k]k^n, {k, 0, n}], {n, 1, 20}] (* Geoffrey Critzer, Sep 16 2012 *)
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PROG
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(PARI) x='x+O('x^50); Vec(serlaplace(1/(1 + lambertw(-x*exp(x))))) \\ G. C. Greubel, Nov 10 2017
(PARI) a(n) = sum(k=0, n, binomial(n, k)*k^n); \\ Michel Marcus, Nov 10 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Offset set to 0 and a(0) = 1 prepended by Peter Luschny, Jun 09 2015
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STATUS
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approved
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