A356820 Expansion of e.g.f. exp(-x * exp(3*x)).

1, -1, -5, -10, 73, 1004, 5473, -15562, -746447, -9174088, -41916959, 823985546, 24629093641, 335144105828, 1248594602305, -67564407472426, -2160461588461343, -34957074099518608, -154556217713939903, 10500560586914149250, 409146670525578079801

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

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

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x*exp(3*x))))
(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, (-x)^k/(1-3*k*x)^(k+1)))
(PARI) a(n) = sum(k=0, n, (-1)^k*(3*k)^(n-k)*binomial(n, k));

Crossrefs

Cf. A292952, A356813, A356819.

Sequence in context: A156102 A120834 A089745 * A358491 A316305 A317260

Adjacent sequences: A356817 A356818 A356819 * A356821 A356822 A356823

Keyword

sign

Author

Seiichi Manyama, Aug 29 2022

Status

approved