A347022 Expansion of e.g.f. 1 / (1 - 5 * log(1 + x))^(1/5).

1, 1, 5, 50, 720, 13650, 320370, 8967720, 291538080, 10795026840, 448484788680, 20658543923280, 1044915105622800, 57572197848878400, 3432143603792520000, 220109018869587398400, 15110184224165199667200, 1105545474191480800492800, 85881534014930659599571200

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = Sum_{k=0..n} Stirling1(n,k) * A008548(k).

a(n) ~ n! * exp(1/25) / (Gamma(1/5) * 5^(1/5) * n^(4/5) * (exp(1/5) - 1)^(n + 1/5)). - Vaclav Kotesovec, Aug 14 2021

a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(k-1) * (5 - 4*k/n) * (k-1)! * binomial(n,k) * a(n-k). - Seiichi Manyama, Sep 11 2023

Mathematica

nmax = 18; CoefficientList[Series[1/(1 - 5 Log[1 + x])^(1/5), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[StirlingS1[n, k] 5^k Pochhammer[1/5, k], {k, 0, n}], {n, 0, 18}]

Crossrefs

Cf. A006252, A008548, A320343, A346984, A346987, A347020, A347021, A347023.

Sequence in context: A185272 A141316 A217794 * A093146 A049393 A047054

Adjacent sequences: A347019 A347020 A347021 * A347023 A347024 A347025

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 11 2021

Status

approved