A372461 Coefficient of x^n in the expansion of 1 / ( (1-x) * (1-x-x^3) )^(2*n).

1, 4, 36, 370, 4012, 44814, 510198, 5886206, 68579020, 805045276, 9507007686, 112817021332, 1344160003030, 16069300956726, 192662610805386, 2315694030560640, 27893938099222316, 336643301659031102, 4069747367955175236, 49274614400855690158

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = Sum_{k=0..floor(n/3)} binomial(2*n+k-1,k) * binomial(5*n-2*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-x^3)^2 ). See A368968.

Prog

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

Crossrefs

Cf. A368968, A372465.

Sequence in context: A163455 A371772 A138736 * A266093 A198638 A358954

Adjacent sequences: A372458 A372459 A372460 * A372462 A372463 A372464

Keyword

nonn

Author

Seiichi Manyama, May 01 2024

Status

approved