A370243 Coefficient of x^n in the expansion of ( 1/(1-x) * (1+x^2)^2 )^n.

1, 1, 7, 28, 143, 701, 3580, 18376, 95471, 499231, 2626607, 13883904, 73681316, 392323868, 2094932728, 11214085328, 60157698287, 323325959395, 1740682221829, 9385343934124, 50671846382743, 273913020523933, 1482311190765896, 8029798017622048, 43538300361416708

Offset

0,3

Links

Table of n, a(n) for n=0..24.

Formula

a(n) = Sum_{k=0..floor(n/2)} binomial(2*n,k) * binomial(2*n-2*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) / (1+x^2)^2 ). See A369226.

Prog

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

Crossrefs

Cf. A240688, A370244.

Cf. A369226.

Sequence in context: A290356 A025030 A001554 * A370103 A359723 A026664

Adjacent sequences: A370240 A370241 A370242 * A370244 A370245 A370246

Keyword

nonn

Author

Seiichi Manyama, Feb 13 2024

Status

approved