A364167 Expansion of g.f. A(x) satisfying A(x) = 1 + x * A(x)^3 * (1 + A(x)^3).

1, 2, 18, 234, 3570, 59586, 1053570, 19392490, 367677090, 7131417282, 140834140722, 2822214963882, 57243994984722, 1172991472484610, 24245748916730658, 504935751379031082, 10584721220759172162, 223163804001804187266, 4729176407109705542994, 100676187744957784842090

Offset: 0

Author

Seiichi Manyama, Jul 13 2023

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..737 (first 50 terms from Christian N. Hofmann)

Crossrefs

Cf. A144097, A153231, A363311.

Programs

Maple

a:= n-> sum(binomial(n, k)*binomial(3*n+3*k+1, n)/(3*n+3*k+1), k=0..n):
seq(a(n), n=0..49); # Christian N. Hofmann, Jul 14 2023

PARI

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

Formula

a(n) = Sum_{k=0..n} binomial(n,k) * binomial(3*n+3*k+1,n)/(3*n+3*k+1).