A369480 Expansion of (1/x) * Series_Reversion( x / ((1+x)^2 * (1+x+x^2)^3) ).

1, 5, 38, 342, 3379, 35427, 387038, 4358119, 50222276, 589439699, 7021368716, 84669873678, 1031603223880, 12679812357672, 157038146685360, 1957792379658934, 24549963008189965, 309435808369427643, 3918185776941808956, 49818464846052855850, 635788103792527271239

Offset: 0

Author

Seiichi Manyama, Jan 23 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A365128, A369479.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^2*(1+x+x^2)^3))/x)

PARI

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

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(3*n+3,k) * binomial(5*n-k+5,n-2*k).