A365147 G.f. satisfies A(x) = ( 1 + x*A(x)^2 / (1 - x*A(x)) )^3.

1, 3, 24, 244, 2802, 34629, 449509, 6043716, 83433402, 1175735326, 16843576440, 244578817557, 3591620791296, 53247623771787, 795901064582970, 11981065741802125, 181478799047422047, 2763977213867989929, 42301686984305340008

Offset: 0

Author

Seiichi Manyama, Aug 23 2023

Keywords

• nonn

Crossrefs

Cf. A001003, A365146.

Programs

PARI

a(n, s=1, 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).