A365154 G.f. satisfies A(x) = ( 1 + x*A(x)^2*(1 + x*A(x)) )^3.

1, 3, 24, 241, 2739, 33513, 430777, 5736027, 78428376, 1094690208, 15533884197, 223429310925, 3250094373788, 47730565667898, 706726767511254, 10538728632234471, 158132963455869912, 2385819265581499593, 36171764848848749205, 550803320282727312804

Offset: 0

Author

Seiichi Manyama, Aug 23 2023

Keywords

• nonn

Crossrefs

Cf. A001002, A365153.

Programs

PARI

a(n, s=1, t=3) = 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).