A369078 Expansion of (1/x) * Series_Reversion( x * (1+x^2/(1-x))^3 ).

1, 0, -3, -3, 21, 54, -157, -828, 816, 11684, 5352, -151407, -288759, 1737498, 6671607, -15789371, -122051205, 58021488, 1935857500, 1977087345, -26913144267, -70826569596, 314853424458, 1586212109946, -2594198888498, -29124507344868, -2575010176581

Offset

0,3

Links

Table of n, a(n) for n=0..26.

Index entries for reversions of series

Formula

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1+x^2/(1-x))^3)/x)
(PARI) a(n, s=2, t=3, u=-3) = 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. A179848, A369081.

Cf. A369013.

Sequence in context: A172485 A230647 A130723 * A209528 A369751 A214778

Adjacent sequences: A369075 A369076 A369077 * A369079 A369080 A369081

Keyword

sign

Author

Seiichi Manyama, Jan 12 2024

Status

approved