A381758 Expansion of exp( Sum_{k>=1} binomial(9*k-1,2*k-1) * x^k/k ).

1, 8, 372, 24732, 1925394, 163883548, 14773987638, 1386341339430, 133994232166575, 13248555929274096, 1333732204895318366, 136243562694021684648, 14087033746990654649067, 1471456489458490198994856, 155042502964505871862313879, 16459391575059417875255359878

Offset: 0

Author

Seiichi Manyama, Mar 06 2025

Keywords

• nonn
• easy

Crossrefs

Cf. A006013, A079489, A182960, A381751, A381752, A381753, A381757.

Cf. A300387.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(exp(sum(k=1, N, binomial(9*k-1, 2*k-1)*x^k/k)))

Formula

a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} binomial(9*k-1,2*k-1) * a(n-k).

G.f.: B(x)^2, where B(x) is the g.f. of A300387.