A370271 Coefficient of x^n in the expansion of 1/( (1-x)^3 * (1-x^2)^3 )^n.

1, 3, 27, 246, 2379, 23628, 239058, 2450052, 25351755, 264270765, 2771024652, 29194911342, 308813298690, 3277454178144, 34883317836240, 372195546176496, 3979793738688075, 42635773396647054, 457529396858568837, 4917191231017846902, 52917857164300253004

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = Sum_{k=0..floor(n/2)} binomial(3*n+k-1,k) * binomial(4*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)^3 * (1-x^2)^3 ). See A368079.

Prog

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

Crossrefs

Cf. A368079.

Sequence in context: A037651 A037770 A037658 * A163474 A235373 A361895

Adjacent sequences: A370268 A370269 A370270 * A370272 A370273 A370274

Keyword

nonn

Author

Seiichi Manyama, Feb 13 2024

Status

approved