OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..350
FORMULA
a(n) = Sum_{k=0..n} |Stirling1(n,k)| * A008548(k).
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
For n > 0, a(n) = Sum_{k=1..n} (n!/(n-k)!)*(5/k-4/n)*a(n-k). - Tani Akinari, Aug 27 2023
MATHEMATICA
nmax = 18; CoefficientList[Series[1/(1 + 5 Log[1 - x])^(1/5), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[Abs[StirlingS1[n, k]] 5^k Pochhammer[1/5, k], {k, 0, n}], {n, 0, 18}]
PROG
(Maxima) a[n]:=if n=0 then 1 else sum(n!/(n-k)!*(5/k-4/n)*a[n-k], k, 1, n);
makelist(a[n], n, 0, 50); /* Tani Akinari, Aug 27 2023 */
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 11 2021
STATUS
approved