A369232 Expansion of (1/x) * Series_Reversion( x * (1-x)^3 / (1-x+x^3)^3 ).

1, 0, 0, 3, 3, 3, 33, 72, 120, 583, 1731, 3888, 13759, 44775, 119793, 381220, 1250328, 3682284, 11455153, 37174428, 114947724, 359381467, 1157319135, 3663615552, 11581104121, 37220909916, 119192219799, 380580143110, 1225279436706, 3948906772872, 12705801908002

Offset

0,4

Links

Table of n, a(n) for n=0..30.

Index entries for reversions of series

Formula

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

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec(serreverse(x*(1-x)^3/(1-x+x^3)^3)/x)
(PARI) a(n, s=3, t=3, u=3) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial((u-t+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);

Crossrefs

Cf. A366052, A369231.

Cf. A369081.

Sequence in context: A372019 A369081 A346909 * A369014 A025549 A124013

Adjacent sequences: A369229 A369230 A369231 * A369233 A369234 A369235

Keyword

nonn

Author

Seiichi Manyama, Jan 17 2024

Status

approved