A370619 Coefficient of x^n in the expansion of ( (1-x) / (1-x-x^2) )^(2*n).

1, 0, 4, 6, 44, 120, 610, 2114, 9468, 36384, 155644, 626450, 2638994, 10856924, 45565118, 189579786, 796023260, 3333362040, 14022032560, 58960463548, 248542728364, 1048148750060, 4427187324102, 18712146312998, 79177190666034, 335259593600120, 1420797366753600

Offset

0,3

Links

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

Formula

a(n) = Sum_{k=0..floor(n/2)} binomial(2*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)^2 / (1-x)^2 ). See A368957.

Prog

(PARI) a(n, s=2, t=2, u=2) = 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. A370617, A370618.

Cf. A368957.

Sequence in context: A012908 A306842 A284634 * A077100 A012935 A013166

Adjacent sequences: A370616 A370617 A370618 * A370620 A370621 A370622

Keyword

nonn

Author

Seiichi Manyama, May 01 2024

Status

approved