A347019 - OEIS

%I #20 Sep 07 2023 08:47:41

%S 1,1,8,114,2358,64074,2157828,86714592,4049302404,215458069428,

%T 12867377875632,852254389954296,61998666080311800,4914000741835488744,

%U 421488717980664846960,38897664480760253351904,3843081247426270376211216,404727487161912602921083536

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

%C 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

%H Seiichi Manyama, <a href="/A347019/b347019.txt">Table of n, a(n) for n = 0..343</a>

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

%F 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

%t nmax = 17; CoefficientList[Series[1/(1 + 6 Log[1 - x])^(1/6), {x, 0, nmax}], x] Range[0, nmax]!

%t Table[Sum[Abs[StirlingS1[n, k]] 6^k Pochhammer[1/6, k], {k, 0, n}], {n, 0, 17}]

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

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Aug 11 2021