A368974 Expansion of (1/x) * Series_Reversion( x * (1-x) * (1-x+x^3)^2 ).

1, 3, 15, 89, 580, 4009, 28857, 213967, 1622869, 12531090, 98171544, 778364379, 6233789872, 50355710215, 409790010350, 3356429972859, 27647745771339, 228890532343859, 1903475080613014, 15893483726218904, 133190665385526309, 1119863488613216952

Offset

0,2

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)} (-1)^k * binomial(2*n+k+1,k) * binomial(4*n-2*k+2,n-3*k).

Prog

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

Crossrefs

Cf. A368970, A368976.

Cf. A368966.

Sequence in context: A287511 A231257 A074541 * A074550 A205576 A173695

Adjacent sequences: A368971 A368972 A368973 * A368975 A368976 A368977

Keyword

nonn

Author

Seiichi Manyama, Jan 10 2024

Status

approved