A352376 Expansion of e.g.f. exp(1 - (1 + x) * exp(x)).

1, -2, 1, 6, -2, -58, -91, 732, 4365, -1468, -140682, -685886, 1791101, 43923266, 216543097, -939472974, -22047365454, -127801626362, 541608607233, 16524264652568, 124850392700061, -279906371211584, -16968403342944782, -176737444660619046

Offset: 0

Author

Seiichi Manyama, Mar 15 2022

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..554

Crossrefs

Cf. A209801, A345652.

Programs

Mathematica

With[{nn=30},CoefficientList[Series[Exp[1-(1+x)Exp[x]],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Oct 11 2024 *)

PARI

my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(1-(1+x)*exp(x))))

PARI

a(n) = if(n==0, 1, -sum(k=1, n, (k+1)*binomial(n-1, k-1)*a(n-k)));

Formula

a(0) = 1; a(n) = -Sum_{k=1..n} (k+1) * binomial(n-1,k-1) * a(n-k).