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

0,2

Links

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

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).

Prog

(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));

Crossrefs

Cf. A356815, A356818.

Cf. A351737, A356813.

Sequence in context: A091752 A078078 A006831 * A016414 A049337 A049801

Adjacent sequences: A356813 A356814 A356815 * A356817 A356818 A356819

Keyword

sign

Author

Seiichi Manyama, Aug 29 2022

Status

approved