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

0,2

Links

Table of n, a(n) for n=0..18.

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).

Prog

(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));

Crossrefs

Cf. A365150, A365151.

Sequence in context: A229299 A365158 A178016 * A372087 A357770 A372105

Adjacent sequences: A365149 A365150 A365151 * A365153 A365154 A365155

Keyword

nonn

Author

Seiichi Manyama, Aug 23 2023

Status

approved