A369299 Expansion of (1/x) * Series_Reversion( x * (1-x) * (1-x^3)^3 ).

1, 1, 2, 8, 29, 105, 417, 1719, 7181, 30603, 132736, 582790, 2585352, 11575613, 52237278, 237328704, 1084701387, 4983867447, 23007263941, 106658256768, 496336303014, 2317687534865, 10856677523580, 51001805706435, 240225121539000, 1134240896062656, 5367428039668751

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Index entries for reversions of series

Formula

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

a(n) = (1/(n+1)) * [x^n] 1/( (1-x) * (1-x^3)^3 )^(n+1). - Seiichi Manyama, Feb 14 2024

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)*(1-x^3)^3)/x)
(PARI) a(n, s=3, t=3, u=1) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial((u+1)*(n+1)-s*k-2, n-s*k))/(n+1);

Crossrefs

Cf. A369300, A369301.

Cf. A063030, A369296.

Cf. A369268.

Sequence in context: A100477 A302266 A369268 * A011367 A220547 A261774

Adjacent sequences: A369296 A369297 A369298 * A369300 A369301 A369302

Keyword

nonn

Author

Seiichi Manyama, Jan 18 2024

Status

approved