login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Expansion of e.g.f. 1 / (1 + 5 * log(1 - x))^(1/5).
7

%I #27 Sep 07 2023 08:47:33

%S 1,1,7,86,1524,35370,1015590,34757400,1381147440,62498177880,

%T 3172764322680,178566159846480,11034757650750960,742773843654742080,

%U 54094804600076176320,4238009228531321452800,355400361455423327193600,31764402860426288679456000,3014207878695233997923193600

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

%H Seiichi Manyama, <a href="/A346987/b346987.txt">Table of n, a(n) for n = 0..350</a>

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

%F a(n) ~ n! * exp(n/5) / (Gamma(1/5) * 5^(1/5) * n^(4/5) * (exp(1/5) - 1)^(n + 1/5)). - _Vaclav Kotesovec_, Aug 14 2021

%F For n > 0, a(n) = Sum_{k=1..n} (n!/(n-k)!)*(5/k-4/n)*a(n-k). - _Tani Akinari_, Aug 27 2023

%t nmax = 18; CoefficientList[Series[1/(1 + 5 Log[1 - x])^(1/5), {x, 0, nmax}], x] Range[0, nmax]!

%t Table[Sum[Abs[StirlingS1[n, k]] 5^k Pochhammer[1/5, k], {k, 0, n}], {n, 0, 18}]

%o (Maxima) a[n]:=if n=0 then 1 else sum(n!/(n-k)!*(5/k-4/n)*a[n-k],k,1,n);

%o makelist(a[n],n,0,50); /* _Tani Akinari_, Aug 27 2023 */

%Y Cf. A007840, A008548, A346978, A346984, A347015, A347016, A347019.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Aug 11 2021