A356815 Expansion of e.g.f. exp(-x * (exp(2*x) + 1)).

1, -2, 0, 4, 32, 48, -608, -6400, -24064, 163072, 3567104, 28394496, 6535168, -3250745344, -50725740544, -344530853888, 2476610551808, 110057610608640, 1655672654135296, 9616664975114240, -195178079811272704, -6998474114188967936, -110894925369151848448

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..499

Formula

G.f.: Sum_{k>=0} (-x)^k / (1 - (2*k-1)*x)^(k+1).

a(n) = Sum_{k=0..n} (-1)^k * (2*k-1)^(n-k) * binomial(n,k).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x*(exp(2*x)+1))))
(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, (-x)^k/(1-(2*k-1)*x)^(k+1)))
(PARI) a(n) = sum(k=0, n, (-1)^k*(2*k-1)^(n-k)*binomial(n, k));

Crossrefs

Cf. A356816, A356818.

Cf. A240165, A351736, A356812.

Sequence in context: A245695 A374286 A069025 * A352554 A352563 A145962

Adjacent sequences: A356812 A356813 A356814 * A356816 A356817 A356818

Keyword

sign

Author

Seiichi Manyama, Aug 29 2022

Status

approved