A365152 G.f. satisfies A(x) = ( 1 + x*A(x)^2 / (1 - x*A(x))^3 )^3.

1, 3, 30, 361, 4887, 71064, 1084338, 17127921, 277691055, 4594624095, 77271742056, 1317037554924, 22699836814548, 394961294853852, 6928051002350154, 122384261274499665, 2175295243858562031, 38875484049230706129, 698131263508514451678

Offset: 0

Author

Seiichi Manyama, Aug 23 2023

Keywords

• nonn

Crossrefs

Cf. A365150, A365151.

Programs

PARI

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

Formula

If g.f. satisfies A(x) = ( 1 + x*A(x)^2 / (1 - x*A(x))^s )^t, then a(n) = Sum_{k=0..n} binomial(t*(n+k+1),k) * binomial(n+(s-1)*k-1,n-k)/(n+k+1).