A346987 Expansion of e.g.f. 1 / (1 + 5 * log(1 - x))^(1/5).

1, 1, 7, 86, 1524, 35370, 1015590, 34757400, 1381147440, 62498177880, 3172764322680, 178566159846480, 11034757650750960, 742773843654742080, 54094804600076176320, 4238009228531321452800, 355400361455423327193600, 31764402860426288679456000, 3014207878695233997923193600

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

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

Sequence in context: A296639 A220306 A344106 * A092586 A048363 A254473

Adjacent sequences: A346984 A346985 A346986 * A346988 A346989 A346990

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 11 2021

Status

approved