A370245 Coefficient of x^n in the expansion of ( 1/(1-x)^2 * (1+x^2)^3 )^n.

1, 2, 16, 110, 828, 6352, 49696, 393668, 3148316, 25362992, 205519616, 1673272702, 13677016932, 112165564656, 922490228032, 7605558361960, 62839438825244, 520180768020464, 4313251202569216, 35818392770702104, 297846498752214128, 2479748570715505472

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = Sum_{k=0..floor(n/2)} binomial(3*n,k) * binomial(3*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)^2 / (1+x^2)^3 ). See A369263.

Prog

(PARI) a(n, s=2, t=3, u=2) = sum(k=0, n\s, binomial(t*n, k)*binomial((u+1)*n-s*k-1, n-s*k));

Crossrefs

Cf. A288470, A360242.

Cf. A369263.

Sequence in context: A207435 A301940 A359758 * A370270 A058121 A117627

Adjacent sequences: A370242 A370243 A370244 * A370246 A370247 A370248

Keyword

nonn

Author

Seiichi Manyama, Feb 13 2024

Status

approved