A353547 Expansion of e.g.f. -log(1-3*x) * exp(x)/3.

0, 1, 5, 30, 256, 2969, 43665, 776194, 16159304, 385353945, 10353609253, 309401268494, 10177974023448, 365446593201793, 14220922741157249, 596150920955286402, 26783000840591098288, 1283751796983110068817, 65389160400251577565797

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

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

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

a(n) ~ (n-1)! * exp(1/3) * 3^(n-1). - Vaclav Kotesovec, Jun 08 2022

Prog

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

Crossrefs

Cf. A002104, A353546, A353548, A353549.

Cf. A346395.

Essentially partial sums of A010845.

Sequence in context: A346681 A279155 A245247 * A199131 A342389 A344525

Adjacent sequences: A353544 A353545 A353546 * A353548 A353549 A353550

Keyword

nonn

Author

Seiichi Manyama, May 27 2022

Status

approved