A355411 Expansion of e.g.f. 1/(3 - exp(2*x) - exp(3*x)).

1, 5, 63, 1175, 29211, 907775, 33852603, 1472830175, 73232729451, 4096474833695, 254608472798043, 17407167078420575, 1298290575826434891, 104900562662494154015, 9127848307446874753083, 850985644429074730049375, 84626187772620135685119531

Offset: 0

Author

Seiichi Manyama, Jul 01 2022

Keywords

• nonn

Crossrefs

Cf. A355380, A355409.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(3-exp(2*x)-exp(3*x))))

PARI

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, (3^j+2^j)*binomial(i, j)*v[i-j+1])); v;

Formula

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

a(n) ~ n! / ((9 - r^2) * log(r)^(n+1)), where r = (-1 + 2*cosh(log((79 + 9*sqrt(77))/2)/3))/3. - Vaclav Kotesovec, Jul 01 2022