A381752 Expansion of exp( Sum_{k>=1} binomial(10*k-1,2*k-1) * x^k/k ).

1, 9, 525, 44067, 4338765, 467396050, 53346810991, 6339179481480, 775994115988525, 97182642466115275, 12392633418043399130, 1603634650155295053250, 210047857493659698690575, 27795006677556725604853840, 3710220786174094422360657000, 498998879378383167317202612400

Offset: 0

Author

Seiichi Manyama, Mar 06 2025

Keywords

• nonn
• easy

Crossrefs

Cf. A006013, A079489, A182960, A381751, A381753, A381757, A381758.

Cf. A381746.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(exp(sum(k=1, N, binomial(10*k-1, 2*k-1)*x^k/k)))

Formula

a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} binomial(10*k-1,2*k-1) * a(n-k).