A387548 Expansion of (1/x) * Series_Reversion( x * (1 - x)^2 / (1 + x^2 / (1 - x)^2) ).

1, 2, 8, 40, 223, 1328, 8270, 53196, 350689, 2356890, 16088112, 111231068, 777320737, 5481871632, 38963663056, 278836127516, 2007401871253, 14528342252042, 105643734111872, 771446384142220, 5654857789912030, 41594561301510272, 306913604696254276

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Formula

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

a(n) = (1/(n+1)) * [x^n] ((1 + x^2 / (1 - x)^2) / (1 - x)^2)^(n+1).

Prog

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

Crossrefs

Cf. A366049, A369208, A389548.

Sequence in context: A143388 A027282 A006195 * A214763 A219587 A092807

Adjacent sequences: A387545 A387546 A387547 * A387549 A387550 A387551

Keyword

nonn

Author

Seiichi Manyama, Oct 07 2025

Status

approved