A363908 a(n) = exp(-1/5) * Sum_{k>=0} (5*k + 4)^n / (5^k * k!).

1, 5, 30, 225, 2075, 22500, 276875, 3790625, 57050000, 934984375, 16549046875, 314146406250, 6358972578125, 136603266015625, 3101556258593750, 74164388642578125, 1861859526474609375, 48936176077929687500, 1343302192888037109375, 38425435693841064453125, 1143143051078878906250000

Offset: 0

Author

Michael De Vlieger, Jun 27 2023

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..450
• Adam Buck, Jennifer Elder, Azia A. Figueroa, Pamela E. Harris, Kimberly Harry, and Anthony Simpson, Flattened Stirling Permutations, arXiv:2306.13034 [math.CO], 2023. See p. 14.

Crossrefs

Cf. A007405, A050488, A355164, A355167.

Programs

Mathematica

CoefficientList[Series[Exp[4 x + (Exp[5 x] - 1)/5], {x, 0, #}], x]* Range[0, #]! &[21]