A003725 E.g.f.: exp( x * exp(-x) ).

1, 1, -1, -2, 9, -4, -95, 414, 49, -10088, 55521, -13870, -2024759, 15787188, -28612415, -616876274, 7476967905, -32522642896, -209513308607, 4924388011050, -38993940088199, 11731860520780, 3807154270837281

Offset: 0

Author

R. H. Hardin

Keywords

• sign
• easy

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..557
• Bérénice Delcroix-Oger and Clément Dupont, Lie-operads and operadic modules from poset cohomology, arXiv:2505.06094 [math.CO], 2025. See p. 32, Table 3.

Crossrefs

Cf. A000248, A069856, A072034. A215652.

Cf. this sequence (k=1), A292909 (k=2), A292910 (k=3), A292912 (k=4).

Programs

Mathematica

With[{nn=30},CoefficientList[Series[Exp[x Exp[-x]],{x,0,nn}],x]Range[0,nn]!] (* Harvey P. Dale, Oct 20 2011 *)

PARI

Vec(serlaplace(exp(exp(-x) * x))) \\ Charles R Greathouse IV, Sep 26 2017

Formula

a(n) = Sum_{k=0..n} (-k)^(n-k)*binomial(n, k). - Vladeta Jovovic, Mar 15 2003

First column of A215652. - Peter Bala, Sep 14 2012

G.f.: Sum_{k>=0} x^k/(1 + k*x)^(k+1). - Ilya Gutkovskiy, Jun 25 2018