A370616 Coefficient of x^n in the expansion of ( (1-x) / (1-x-x^2) )^n.

1, 0, 2, 3, 14, 35, 125, 371, 1238, 3909, 12847, 41580, 136577, 447187, 1473341, 4855703, 16053830, 53138243, 176233967, 585202261, 1945964079, 6478043120, 21588979876, 72016891508, 240452892569, 803489258285, 2686964354375, 8991840800136, 30110638705889

Offset

0,3

Links

Table of n, a(n) for n=0..28.

Formula

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

The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x * (1-x-x^2) / (1-x) ).

Prog

(PARI) a(n, s=2, t=1, u=1) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial((t-u+1)*n-(s-1)*k-1, n-s*k));

Crossrefs

Cf. A046736, A213684.

Sequence in context: A346606 A059188 A080768 * A203578 A329442 A281486

Adjacent sequences: A370613 A370614 A370615 * A370617 A370618 A370619

Keyword

nonn

Author

Seiichi Manyama, Apr 30 2024

Status

approved