A365153 G.f. satisfies A(x) = ( 1 + x*A(x)^2*(1 + x*A(x)) )^2.

1, 2, 11, 74, 563, 4604, 39524, 351322, 3205699, 29854250, 282615379, 2711494224, 26307568324, 257673017952, 2544420045432, 25303000558890, 253184833958403, 2547251287244918, 25752086767703969, 261480234091024906, 2665405840919762043

Offset: 0

Author

Seiichi Manyama, Aug 23 2023

Keywords

• nonn

Crossrefs

Cf. A001002, A365154.

Programs

PARI

a(n, s=1, t=2) = sum(k=0, n, binomial(t*(n+k+1), k)*binomial(s*k, 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(s*k,n-k)/(n+k+1).