A371398 Expansion of (1/x) * Series_Reversion( x / ( (1+x) * (1+2*x)^3 ) ).

1, 7, 67, 741, 8909, 113107, 1492103, 20251945, 280978681, 3967031839, 56811348235, 823250855181, 12049087175493, 177857857845675, 2644773866954255, 39581787842355409, 595745692419162737, 9011736489133233463, 136932249972928786387

Offset: 0

Author

Seiichi Manyama, Mar 21 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Essentially the same as A243675.

Cf. A034015.

Programs

PARI

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

PARI

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

Formula

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