A372459 Coefficient of x^n in the expansion of 1 / ( (1-x) * (1-x-x^3)^2 )^n.

1, 3, 21, 171, 1469, 12988, 116985, 1067545, 9836541, 91313469, 852701256, 8001080244, 75375985841, 712487600698, 6754115819535, 64185511063246, 611287650124125, 5832863405199183, 55750924705841643, 533676328608473118, 5115556211638071944

Offset

0,2

Links

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

Formula

a(n) = Sum_{k=0..floor(n/3)} binomial(2*n+k-1,k) * binomial(4*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) * (1-x-x^3)^2 ). See A368966.

Prog

(PARI) a(n, s=3, t=2, u=1) = 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. A368966.

Sequence in context: A046637 A220103 A132805 * A189475 A331328 A372089

Adjacent sequences: A372456 A372457 A372458 * A372460 A372461 A372462

Keyword

nonn

Author

Seiichi Manyama, May 01 2024

Status

approved