A372465 Coefficient of x^n in the expansion of 1 / ( (1-x) * (1-x+x^3) )^(2*n).

1, 4, 36, 358, 3740, 40194, 439998, 4879326, 54630316, 616194700, 6991215286, 79700776588, 912207989030, 10475536585674, 120641989237890, 1392811194744288, 16114668707519404, 186798818992569818, 2168990381036497812, 25222834639587149890, 293708687012053512870

Offset

0,2

Links

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

Formula

a(n) = Sum_{k=0..floor(n/3)} (-1)^k * 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 A368976.

Prog

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

Crossrefs

Cf. A368976, A372461.

Sequence in context: A189334 A026334 A247562 * A168595 A163455 A371772

Adjacent sequences: A372462 A372463 A372464 * A372466 A372467 A372468

Keyword

nonn

Author

Seiichi Manyama, May 01 2024

Status

approved