A371387 Expansion of (1/x) * Series_Reversion( x * (1-4*x)^3 / (1-x) ).

1, 11, 205, 4647, 116873, 3135635, 87924597, 2545845135, 75534363601, 2284439539035, 70166186106333, 2182759455876663, 68630655620066265, 2177561996773904483, 69632831106680348165, 2241852665024904670239, 72608750028928583936673

Offset: 0

Author

Seiichi Manyama, Mar 20 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A131763, A371386.

Cf. A371365.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-4*x)^3/(1-x))/x)

PARI

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

Formula

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