A381907 Expansion of (1/x) * Series_Reversion( x / ((1+x)^3 * B(x)) ), where B(x) is the g.f. of A001764.

1, 4, 25, 197, 1783, 17646, 185622, 2039617, 23149542, 269367631, 3196544816, 38539697456, 470773651286, 5813914938293, 72470441063067, 910587733474165, 11521140613913305, 146659482494039073, 1876975898990490298, 24137070792680577688, 311724732112458291945

Offset: 0

Author

Seiichi Manyama, Mar 10 2025

Keywords

• nonn

Crossrefs

Cf. A381905, A381906.

Cf. A001764, A381882.

Programs

PARI

a(n) = sum(k=0, n, binomial(n+3*k+1, k)*binomial(3*n+3, n-k)/(n+3*k+1));

Formula

G.f. A(x) satisfies A(x) = (1 + x*A(x))^3 * B(x*A(x)).

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