A379139 G.f. A(x) satisfies A(x) = ( (1 + x*A(x)^(1/3)) * (1 + x*A(x)^(2/3)) )^3.

1, 6, 33, 185, 1065, 6276, 37711, 230277, 1425180, 8920915, 56382321, 359325561, 2306603557, 14900834070, 96801107625, 631995206707, 4144614844047, 27289670546697, 180339237891360, 1195684324845420, 7951560286540908, 53025939926690233, 354509890878236583

Offset: 0

Author

Seiichi Manyama, Dec 15 2024

Keywords

• nonn

Crossrefs

Cf. A003517, A007863.

Programs

PARI

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

Formula

G.f.: A(x) = B(x)^3 where B(x) is the g.f. of A007863.

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