A383633 Expansion of 1/( Product_{k=0..10} (1 - (11*k+1) * x) )^(1/11).

1, 56, 3741, 277256, 22052713, 1846878936, 160878051401, 14454374710216, 1331486959280259, 125190717874655720, 11973642784650273211, 1161838196321182959096, 114133506709827074843495, 11331528323810252967417064, 1135444330405820622163425351, 114694796036872449398436891896

Offset: 0

Author

Seiichi Manyama, May 03 2025

Keywords

• nonn

Comments

In general, if m > 0 and g.f. = 1/(Product_{k=0..m-1} (1 - (m*k+1)*x))^(1/m), then a(n) ~ (m*(m-1) + 1)^(n + 1 - 1/m) / (Gamma(1/m) * Gamma(m+1)^(1/m) * m^(1 - 2/m) * n^(1 - 1/m)). - Vaclav Kotesovec, Aug 18 2025

Crossrefs

Cf. A383627, A383628, A383629, A383630, A383631, A383632.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(1/prod(k=0, 10, 1-(11*k+1)*x)^(1/11))

Formula

a(n) ~ 3^(n + 6/11) * 37^(n + 10/11) / (Gamma(1/11) * 2^(8/11) * 5^(2/11) * 7^(1/11) * 11^(10/11) * n^(10/11)). - Vaclav Kotesovec, May 12 2025