A094869 E.g.f.: exp(5x)/(1-5x)^(1/5).

1, 6, 41, 356, 4401, 78826, 1893481, 56341416, 1978638881, 79749105326, 3622010623401, 182895318578956, 10160561511881041, 615728464210461906, 40414538467581457001, 2855999961062529064976, 216180544920721807887681

Offset: 0

Author

Philippe Deléham, Jun 16 2004

Keywords

• nonn

Comments

Sum_{k = 0..n} A046716(n,k)*x^k give A000522(n), A081367(n), A094822(n), A094856(n) for x = 1, 2, 3, 4 respectively.

Programs

Mathematica

With[{nn=20},CoefficientList[Series[Exp[5x]/(1-5x)^(1/5),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, May 19 2014 *)

Formula

a(n) = Sum_{k = 0..n} A046716(n, k)*5^k.

Conjectured to be D-finite with recurrence: a(n) +(-5*n-1)*a(n-1) +25*(n-1)*a(n-2)=0. - R. J. Mathar, Nov 15 2019

a(n) ~ sqrt(2*Pi) * 5^n * n^(n - 3/10) / (Gamma(1/5) * exp(n-1)). - Vaclav Kotesovec, Nov 19 2021