A383632 Expansion of 1/( Product_{k=0..8} (1 - (9*k+1) * x) )^(1/9).

1, 37, 1639, 80623, 4257424, 236721412, 13688641144, 816291120808, 49895692924132, 3112177949225236, 197407027057353724, 12699858803178669148, 826900665838817386456, 54398158759680212197576, 3610650035912536155468808, 241521616482786052388206408, 16265890564063100473094045146

Offset: 0

Author

Seiichi Manyama, May 03 2025

Keywords

• nonn

Crossrefs

Cf. A383627, A383628, A383629, A383630, A383631, A383633.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(1/prod(k=0, 8, 1-(9*k+1)*x)^(1/9))

Formula

a(n) ~ 4480^(8/9) * 73^(n + 8/9) / (40320 * Gamma(1/9) * n^(8/9)). - Vaclav Kotesovec, Aug 18 2025