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A069856
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E.g.f.: exp(x)/(1+LambertW(x)).
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21
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1, 0, 3, -17, 169, -2079, 31261, -554483, 11336753, -262517615, 6791005621, -194103134499, 6074821125385, -206616861429575, 7588549099814957, -299320105069298459, 12619329503201165281, -566312032570838608863, 26952678355224681891685
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OFFSET
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0,3
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COMMENTS
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The |a(n)| is the number of functions f:{1,2,...,n}->{1,2,...,n} such that the digraph representation of f has no isolated vertices. (* Geoffrey Critzer, Nov 13 2011 *)
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REFERENCES
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sci.math article 3CBC2B66.224E(AT)olympus.mons
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LINKS
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FORMULA
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a(n) = n! * Sum_{k=0..n} (-1)^k*k^k/(k!*(n - k)!).
abs(a(n)) ~ (exp(1)*n-1/2)/exp(1+exp(-1)) * n^(n-1). - Vaclav Kotesovec, Nov 27 2012
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MATHEMATICA
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t = Sum[n^(n - 1) x^n/n!, {n, 1, 20}]; Range[0, 20]! CoefficientList[Series[Exp[-x]/(1 - t), {x, 0, 20}], x] (* Geoffrey Critzer, Nov 13 2011 *)
Range[0, 18]! CoefficientList[ Series[ Exp[x]/(1 + LambertW[x]), {x, 0, 18}], x] (* Robert G. Wilson v, Nov 28 2012 *)
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PROG
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(PARI) x='x+O('x^50); Vec(serlaplace(exp(x)/(1+lambertw(x)))) \\ G. C. Greubel, Jun 11 2017
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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Joe Keane (jgk(AT)jgk.org), May 03 2002
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STATUS
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approved
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