A383631 Expansion of 1/( Product_{k=0..7} (1 - (8*k+1) * x) )^(1/8).

1, 29, 1009, 39005, 1618849, 70741469, 3214527633, 150606953757, 7231305564225, 354221417305757, 17641204276036657, 890872808134921949, 45521466404971069921, 2349568589682742349405, 122328082368695017498321, 6416984703345086646305181, 338833672698752842286404737

Offset: 0

Author

Seiichi Manyama, May 03 2025

Keywords

• nonn

Crossrefs

Cf. A383627, A383628, A383629, A383630, A383632, A383633.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(1/prod(k=0, 7, 1-(8*k+1)*x)^(1/8))

Formula

a(n) ~ 3^(n + 5/8) * 19^(n + 7/8) / (Gamma(1/8) * 2^(25/8) * 5^(1/8) * 7^(1/8) * n^(7/8)). - Vaclav Kotesovec, Aug 18 2025