A370272 Coefficient of x^n in the expansion of 1/( (1-x) * (1-x^3) )^n.

1, 1, 3, 13, 51, 201, 819, 3382, 14067, 58927, 248303, 1051128, 4466787, 19043766, 81418746, 348936288, 1498601459, 6448162221, 27791057997, 119954739879, 518451715551, 2243481128020, 9718784202240, 42143960004750, 182917942802595, 794589638379576

Offset: 0

Author

Seiichi Manyama, Feb 13 2024

Keywords

• nonn

Crossrefs

Cf. A063030.

Programs

PARI

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

Formula

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