A365148 G.f. satisfies A(x) = ( 1 + x*A(x)^2 / (1 - x*A(x))^2 )^2.

1, 2, 13, 102, 898, 8484, 84061, 861918, 9068950, 97366812, 1062425010, 11747773372, 131350499044, 1482494173128, 16867912278237, 193273940978574, 2228186999313678, 25827663921909228, 300825086742672934, 3519001122784601524, 41325186203051759324

Offset: 0

Author

Seiichi Manyama, Aug 23 2023

Keywords

• nonn

Crossrefs

Cf. A011270, A365149.

Cf. A365120, A365133.

Programs

PARI

a(n, s=2, t=2) = 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).