A365132 G.f. satisfies A(x) = (1 + x*A(x)*(1 + x*A(x))^3)^3.

1, 3, 21, 163, 1410, 12954, 124197, 1228269, 12438504, 128338224, 1344328020, 14258394921, 152820980120, 1652596758738, 18008899150278, 197566103218974, 2180167982738235, 24183969704272350, 269513577777159816, 3016075156973165367, 33879382051847177781

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

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

Prog

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

Crossrefs

Cf. A364742, A365131.

Cf. A001764.

Sequence in context: A058194 A179815 A118353 * A371817 A262977 A361375

Adjacent sequences: A365129 A365130 A365131 * A365133 A365134 A365135

Keyword

nonn

Author

Seiichi Manyama, Aug 23 2023

Status

approved