A386773 Expansion of (1/x) * Series_Reversion( x * (1-3*x)^2 / (1+2*x)^3 ).

1, 12, 219, 4778, 115011, 2945982, 78764484, 2172877458, 61393035171, 1767592420152, 51672186100899, 1529632003964688, 45760966837725556, 1381338453812353272, 42020564167060633464, 1286902432396816483218, 39645674268979326240291, 1227773019572168363776092

Offset: 0

Author

Seiichi Manyama, Aug 02 2025

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A386722.

Programs

PARI

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

PARI

a(n) = sum(k=0, n, 2^k*3^(n-k)*binomial(3*(n+1), k)*binomial(3*n-k+1, n-k))/(n+1);

Formula

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

a(n) = (1/(n+1)) * [x^n] ( (1+2*x)^3 / (1-3*x)^2 )^(n+1).