A367261 G.f. satisfies A(x) = 1 + x*A(x) * (1 + x*A(x)^2)^3.

1, 1, 4, 16, 77, 393, 2113, 11761, 67217, 392140, 2325691, 13980390, 84990482, 521623164, 3227679457, 20114056545, 126125100615, 795207084713, 5038166859565, 32059491655921, 204806561028553, 1313023485343009, 8445060537757367, 54476991669555231

Offset: 0

Author

Seiichi Manyama, Nov 11 2023

Keywords

• nonn

Crossrefs

Cf. A137953, A367239.

Programs

PARI

a(n, s=3, t=1, u=2) = sum(k=0, n, binomial(t*k+u*(n-k)+1, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+1));

Formula

If g.f. satisfies A(x) = 1 + x*A(x)^t * (1 + x*A(x)^u)^s, then a(n) = Sum_{k=0..n} binomial(t*k+u*(n-k)+1,k) * binomial(s*k,n-k) / (t*k+u*(n-k)+1).