A353548 Expansion of e.g.f. -log(1-4*x) * exp(x)/4.

0, 1, 6, 47, 540, 8429, 166210, 3952955, 109981816, 3502905369, 125648153278, 5011458069639, 219987094389524, 10538817637744005, 547118005892177018, 30595552548140425747, 1833501625083035349488, 117219490267316310468913

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = n! * Sum_{k=0..n-1} 4^(n-1-k) / ((n-k) * k!).

a(0) = 0, a(1) = 1, a(n) = (4 * n - 3) * a(n-1) - 4 * (n-1) * a(n-2) + 1.

a(n) ~ (n-1)! * exp(1/4) * 4^(n-1). - Vaclav Kotesovec, Jun 08 2022

Prog

(PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-log(1-4*x)*exp(x)/4)))
(PARI) a(n) = n!*sum(k=0, n-1, 4^(n-1-k)/((n-k)*k!));
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=0; v[2]=1; for(i=2, n, v[i+1]=(4*i-3)*v[i]-4*(i-1)*v[i-1]+1); v;

Crossrefs

Cf. A002104, A353546, A353547, A353549.

Cf. A346396.

Essentially partial sums of A056545.

Sequence in context: A307567 A368270 A332238 * A192887 A321190 A320403

Adjacent sequences: A353545 A353546 A353547 * A353549 A353550 A353551

Keyword

nonn

Author

Seiichi Manyama, May 27 2022

Status

approved