A356818 Expansion of e.g.f. exp(-x * (exp(x) + 1)).

1, -2, 2, 1, 0, -17, -32, 103, 976, 2287, -12816, -143585, -481016, 2339335, 39769720, 209863327, -397553376, -16949434913, -142681662368, -233212601153, 9138353475736, 128343346833463, 702261255539496, -4251314594919617, -135331386127555856

Offset: 0

Author

Seiichi Manyama, Aug 29 2022

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..558

Crossrefs

Cf. A356815, A356816.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x*(exp(x)+1))))

PARI

my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, (-x)^k/(1-(k-1)*x)^(k+1)))

PARI

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

Formula

G.f.: Sum_{k>=0} (-x)^k / (1 - (k-1)*x)^(k+1).

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