A367260 G.f. satisfies A(x) = 1 + x*A(x)^3 * (1 + x*A(x))^3.

1, 1, 6, 36, 251, 1881, 14817, 120950, 1014042, 8680377, 75552553, 666614637, 5948817600, 53599239101, 486926148000, 4455202562652, 41018936164660, 379747493741643, 3532914858433284, 33012260400580342, 309692626084981245, 2915659701275923491

Offset: 0

Author

Seiichi Manyama, Nov 11 2023

Keywords

• nonn

Crossrefs

Cf. A019497, A361305, A364742.

Cf. A367233.

Programs

PARI

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