A355421 Expansion of e.g.f. exp(Sum_{k=1..3} (exp(k*x) - 1)).

1, 6, 50, 504, 5870, 76872, 1111646, 17522664, 298133054, 5433157512, 105396184478, 2165189912040, 46901678992958, 1067332196912136, 25435754924426270, 633014456504059368, 16411191933603611198, 442258823578968351624

Offset

0,2

Links

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

Formula

a(0) = 1; a(n) = Sum_{k=1..n} (1 + 2^k + 3^k) * binomial(n-1,k-1) * a(n-k).

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=1, 3, exp(k*x)-1))))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, (1+2^j+3^j)*binomial(i-1, j-1)*v[i-j+1])); v;

Crossrefs

Column k=3 of A355423.

Cf. A004701, A306027, A355379, A355380.

Sequence in context: A365189 A303562 A125558 * A005416 A300989 A105617

Adjacent sequences: A355418 A355419 A355420 * A355422 A355423 A355424

Keyword

nonn

Author

Seiichi Manyama, Jul 01 2022

Status

approved