A355081 G.f. A(x) satisfies A(x) = 1 + x * A(3 * x / (1 - x)) / (1 - x).

1, 1, 4, 43, 1279, 108472, 26888677, 19761575473, 43356335678176, 284807217244068223, 5608422162798704960959, 331227791701602557410058404, 58679652813856265804094312228601, 31185477505022553490008128886444268657

Offset: 0

Author

Seiichi Manyama, Jun 18 2022

Keywords

• nonn

Crossrefs

Column k=3 of A306245.

Cf. A000110, A126443, A355082.

Programs

PARI

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, 3^j*binomial(i-1, j)*v[j+1])); v;

Formula

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