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

0,2

Links

Table of n, a(n) for n=0..19.

Index entries for reversions of series

Formula

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

Prog

(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);

Crossrefs

Cf. A082298, A371394.

Cf. A064087.

Sequence in context: A083302 A099342 A051550 * A355163 A300488 A085283

Adjacent sequences: A371390 A371391 A371392 * A371394 A371395 A371396

Keyword

nonn

Author

Seiichi Manyama, Mar 21 2024

Status

approved