A370626 Coefficient of x^n in the expansion of 1 / (1-x-x^3)^(2*n).

1, 2, 10, 62, 402, 2662, 17914, 122040, 839154, 5811758, 40482530, 283311470, 1990464450, 14030571258, 99179197512, 702789627712, 4990636603986, 35506061422530, 253030893941362, 1805893735209486, 12906043894108162, 92346511605008562, 661494201448139850

Offset: 0

Author

Seiichi Manyama, May 01 2024

Keywords

• nonn

Crossrefs

Cf. A368962.

Programs

PARI

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

Formula

a(n) = Sum_{k=0..floor(n/3)} binomial(2*n+k-1,k) * binomial(3*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-x^3)^2 ). See A368962.