A371393 Expansion of (1/x) * Series_Reversion( x * (1-x) / (1+3*x)^2 ).

1, 7, 65, 695, 8081, 99303, 1268961, 16694295, 224617265, 3076621127, 42757939841, 601443961207, 8546453367505, 122502619954855, 1769134504184865, 25716831677125335, 375988660156913265, 5525224188936386055, 81565308431025658305, 1209038650866275440695

Offset: 0

Author

Seiichi Manyama, Mar 21 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A082298, A371394.

Cf. A064087.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)/(1+3*x)^2)/x)

PARI

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

Formula

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