A389550 Expansion of (1/x) * Series_Reversion( x * (1 - x)^2 / (1 + x^3 / (1 - x)^3) ).

1, 2, 7, 31, 156, 848, 4848, 28710, 174505, 1082184, 6819380, 43538377, 281022011, 1830738588, 12021608943, 79486728327, 528752655711, 3536154910106, 23761619146263, 160351080083436, 1086265193393688, 7384325761403944, 50357127973860129, 344403734057180652

Offset

0,2

Links

Table of n, a(n) for n=0..23.

Formula

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

a(n) = (1/(n+1)) * [x^n] ((1 + x^3 / (1 - x)^3) / (1 - x)^2)^(n+1).

Prog

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

Crossrefs

Cf. A366052, A369265, A389549.

Sequence in context: A369214 A302061 A030823 * A389630 A394132 A030873

Adjacent sequences: A389547 A389548 A389549 * A389551 A389552 A389553

Keyword

nonn

Author

Seiichi Manyama, Oct 07 2025

Status

approved