A370624 Coefficient of x^n in the expansion of 1 / (1-x-x^3)^n.

1, 1, 3, 13, 55, 231, 987, 4278, 18711, 82390, 364793, 1622556, 7244419, 32449158, 145747290, 656199048, 2960596359, 13382107227, 60587421882, 274712295550, 1247233045905, 5669390005950, 25798654040580, 117513750346200, 535766200488675, 2444698473079356

Offset: 0

Author

Seiichi Manyama, May 01 2024

Keywords

• nonn

Crossrefs

Cf. A049140.

Programs

PARI

a(n, s=3, t=1, 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(n+k-1,k) * binomial(2*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) ).