A356819 Expansion of e.g.f. exp(-x * exp(2*x)).

1, -1, -3, -1, 41, 239, 229, -8401, -87151, -324577, 3238541, 70271519, 601086265, 142860431, -81504662539, -1393683935281, -10777424809951, 63537986981183, 3552608426329117, 60283510555017023, 441644419610814281, -6191820436867600081

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

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

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

Prog

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

Crossrefs

Cf. A216689, A292952, A356812, A356820.

Sequence in context: A050817 A125082 A307803 * A362166 A136517 A366479

Adjacent sequences: A356816 A356817 A356818 * A356820 A356821 A356822

Keyword

sign

Author

Seiichi Manyama, Aug 29 2022

Status

approved