A365149 G.f. satisfies A(x) = ( 1 + x*A(x)^2 / (1 - x*A(x))^2 )^3.

1, 3, 27, 301, 3780, 51030, 723170, 10611594, 159845946, 2457515235, 38406398016, 608330707740, 9744053489754, 157564967282709, 2568706865998272, 42173100349112852, 696692754641035014, 11572241797209975966, 193153224033985241217

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=2, 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. A011270, A365148.

Cf. A365121, A365134.

Sequence in context: A365156 A372203 A200903 * A318108 A290576 A291315

Adjacent sequences: A365146 A365147 A365148 * A365150 A365151 A365152

Keyword

nonn

Author

Seiichi Manyama, Aug 23 2023

Status

approved