A347019 E.g.f.: 1 / (1 + 6 * log(1 - x))^(1/6).

1, 1, 8, 114, 2358, 64074, 2157828, 86714592, 4049302404, 215458069428, 12867377875632, 852254389954296, 61998666080311800, 4914000741835488744, 421488717980664846960, 38897664480760253351904, 3843081247426270376211216, 404727487161912602921083536

Offset: 0

Author

Ilya Gutkovskiy, Aug 11 2021

Keywords

• nonn

Comments

In general, for k >= 1, if e.g.f. = 1 / (1 + k*log(1 - x))^(1/k), then a(n) ~ n! * exp(n/k) / (Gamma(1/k) * k^(1/k) * n^(1 - 1/k) * (exp(1/k) - 1)^(n + 1/k)). - Vaclav Kotesovec, Aug 14 2021

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..343

Crossrefs

Cf. A007840, A008542, A346978, A346985, A346987, A347015, A347016.

Programs

Mathematica

nmax = 17; CoefficientList[Series[1/(1 + 6 Log[1 - x])^(1/6), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[Abs[StirlingS1[n, k]] 6^k Pochhammer[1/6, k], {k, 0, n}], {n, 0, 17}]

Formula

a(n) = Sum_{k=0..n} |Stirling1(n,k)| * A008542(k).

a(n) ~ n! * exp(n/6) / (Gamma(1/6) * 6^(1/6) * n^(5/6) * (exp(1/6) - 1)^(n + 1/6)). - Vaclav Kotesovec, Aug 14 2021