A369620 Expansion of (1/x) * Series_Reversion( x / (1/(1-x)^3 + x^2) ).

1, 3, 16, 100, 692, 5099, 39240, 311700, 2536490, 21037102, 177176745, 1511211409, 13027296723, 113319727772, 993422328313, 8768003882546, 77848008692270, 694828468698510, 6230785015298952, 56109079416527835, 507188912618646021, 4600432953729579585

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Index entries for reversions of series

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(n+1,k) * binomial(4*n-5*k+2,n-2*k).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1/(1-x)^3+x^2))/x)
(PARI) a(n) = sum(k=0, n\2, binomial(n+1, k)*binomial(4*n-5*k+2, n-2*k))/(n+1);

Crossrefs

Cf. A369618, A369619.

Sequence in context: A360638 A091641 A137572 * A009151 A009007 A000949

Adjacent sequences: A369617 A369618 A369619 * A369621 A369622 A369623

Keyword

nonn

Author

Seiichi Manyama, Jan 27 2024

Status

approved