A381905 Expansion of (1/x) * Series_Reversion( x / ((1+x) * B(x)) ), where B(x) is the g.f. of A001764.

1, 2, 8, 47, 331, 2570, 21204, 182383, 1617163, 14675783, 135643839, 1272434069, 12083390801, 115934171020, 1122129142754, 10943574296787, 107433077283767, 1060800046515405, 10528321010319417, 104972259713887665, 1050936451974803973, 10560662821468607719

Offset: 0

Author

Seiichi Manyama, Mar 10 2025

Keywords

• nonn

Crossrefs

Cf. A381906, A381907.

Cf. A001764, A381911.

Programs

PARI

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

Formula

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

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