A370249 Coefficient of x^n in the expansion of ( 1/(1-x)^2 * (1+x^3)^2 )^n.

1, 2, 10, 62, 394, 2552, 16810, 112114, 754698, 5116832, 34891260, 239036470, 1644001546, 11344059092, 78497737370, 544507428962, 3785080540682, 26360971309824, 183895618774084, 1284778549054704, 8988079638054044, 62955181189933276, 441442177486335002

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) * 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 A369267.

Prog

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

Crossrefs

Cf. A369267, A370215.

Sequence in context: A352277 A155626 A092165 * A370275 A304443 A370626

Adjacent sequences: A370246 A370247 A370248 * A370250 A370251 A370252

Keyword

nonn

Author

Seiichi Manyama, Feb 13 2024

Status

approved