A355425 Expansion of e.g.f. 1/(1 - Sum_{k=1..2} (exp(k*x) - 1)/k).

1, 2, 11, 89, 959, 12917, 208781, 3937019, 84846899, 2057107337, 55416031601, 1642126375199, 53084324076839, 1859037341680157, 70112365228588421, 2833115932639555379, 122113252334984094779, 5592296493425013663377, 271169701559687033317241

Offset: 0

Author

Seiichi Manyama, Jul 01 2022

Keywords

• nonn

Crossrefs

Column k=2 of A355427.

Cf. A004700.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=1, 2, (exp(k*x)-1)/k))))

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-1))*binomial(i, j)*v[i-j+1])); v;

Formula

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