A347013 E.g.f.: exp(x) / (1 - 5 * x)^(1/5).

1, 2, 9, 88, 1361, 28182, 726889, 22414988, 803913441, 32867765002, 1508608850249, 76804271962848, 4294870015118641, 261673684619584862, 17252970318529474089, 1223896705010751194068, 92946073511938131386561, 7523666291578066678172562, 646658551118777059833155209

Offset

0,2

Comments

Binomial transform of A008548.

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = Sum_{k=0..n} binomial(n,k) * A008548(k).

a(n) ~ n! * exp(1/5) * 5^n / (Gamma(1/5) * n^(4/5)). - Vaclav Kotesovec, Aug 14 2021

Maple

g:= proc(n) option remember; `if`(n<2, 1, (5*n-4)*g(n-1)) end:
a:= n-> add(binomial(n, k)*g(k), k=0..n):
seq(a(n), n=0..18);  # Alois P. Heinz, Aug 10 2021

Mathematica

nmax = 18; CoefficientList[Series[Exp[x]/(1 - 5 x)^(1/5), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[Binomial[n, k] 5^k Pochhammer[1/5, k], {k, 0, n}], {n, 0, 18}]
Table[HypergeometricU[1/5, n + 6/5, 1/5]/5^(1/5), {n, 0, 18}]

Crossrefs

Cf. A000522, A008548, A056546, A084262, A088992, A346258, A347012, A347014.

Sequence in context: A135747 A270862 A259794 * A132431 A228509 A361607

Adjacent sequences: A347010 A347011 A347012 * A347014 A347015 A347016

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 10 2021

Status

approved