A370618 Coefficient of x^n in the expansion of ( (1-x) / (1-x-x^2)^2 )^n.

1, 1, 7, 34, 191, 1071, 6154, 35729, 209455, 1236508, 7341577, 43792112, 262230242, 1575391156, 9490934411, 57316715079, 346875036879, 2103174805035, 12773139313516, 77689736488088, 473160660856361, 2885208137132852, 17612514244078288, 107621658416373752

Offset

0,3

Links

Table of n, a(n) for n=0..23.

Formula

a(n) = Sum_{k=0..floor(n/2)} binomial(2*n+k-1,k) * binomial(2*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) ). See A369486.

Prog

(PARI) a(n, s=2, t=2, 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. A370617, A370619.

Cf. A369486.

Sequence in context: A372411 A027233 A117650 * A365474 A273221 A144038

Adjacent sequences: A370615 A370616 A370617 * A370619 A370620 A370621

Keyword

nonn

Author

Seiichi Manyama, Apr 30 2024

Status

approved