A370275 Coefficient of x^n in the expansion of 1/( (1-x)^2 * (1-x^3)^2 )^n.

1, 2, 10, 62, 394, 2552, 16822, 112310, 756874, 5137676, 35076360, 240606082, 1656906550, 11447855850, 79319081054, 550925792312, 3834743187594, 26742188401900, 186802789016908, 1306827910585782, 9154542088193544, 64206944261628146, 450823141806229290

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Formula

a(n) = Sum_{k=0..floor(n/3)} binomial(2*n+k-1,k) * binomial(3*n-3*k-1,n-3*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^3)^2 ). See A369298.

Prog

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

Crossrefs

Cf. A369298.

Sequence in context: A155626 A092165 A370249 * A304443 A370626 A243034

Adjacent sequences: A370272 A370273 A370274 * A370276 A370277 A370278

Keyword

nonn

Author

Seiichi Manyama, Feb 13 2024

Status

approved