A356816 Expansion of e.g.f. exp(-x * (exp(3*x) + 1)).

1, -2, -2, 1, 88, 583, 676, -35597, -519392, -3359393, 19013884, 896435395, 13640180896, 85591357135, -1527872118356, -61100053650053, -1076294742932288, -7610985095240513, 200631806070276988, 9284475508083767059, 200226297062313730816, 1940767272243466116463

Offset: 0

Author

Seiichi Manyama, Aug 29 2022

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..470

Crossrefs

Cf. A356815, A356818.

Cf. A351737, A356813.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x*(exp(3*x)+1))))

PARI

my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, (-x)^k/(1-(3*k-1)*x)^(k+1)))

PARI

a(n) = sum(k=0, n, (-1)^k*(3*k-1)^(n-k)*binomial(n, k));

Formula

G.f.: Sum_{k>=0} (-x)^k / (1 - (3*k-1)*x)^(k+1).

a(n) = Sum_{k=0..n} (-1)^k * (3*k-1)^(n-k) * binomial(n,k).