A371386 Expansion of (1/x) * Series_Reversion( x * (1-4*x)^2 / (1-x) ).

1, 7, 89, 1391, 24209, 450231, 8759337, 176071263, 3627907745, 76217773799, 1626477863801, 35158334302927, 768222871584817, 16940297062253719, 376507441510456905, 8425543117906277055, 189683436162271517505, 4293057440192560395207

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Index entries for reversions of series

Formula

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

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-4*x)^2/(1-x))/x)
(PARI) a(n) = sum(k=0, n, 3^k*binomial(2*n+k+1, k)*binomial(2*n, n-k))/(n+1);

Crossrefs

Cf. A131763, A371387.

Cf. A371364.

Sequence in context: A069661 A069662 A359646 * A295543 A062747 A099719

Adjacent sequences: A371383 A371384 A371385 * A371387 A371388 A371389

Keyword

nonn

Author

Seiichi Manyama, Mar 20 2024

Status

approved