OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..418
FORMULA
a(n) = Sum_{k=1..n} |Stirling1(n,k)|*H(k)*k!, where H(k) is the k-th harmonic number.
a(n) ~ sqrt(2*Pi) * log(n) * n^(n + 1/2) / (exp(1)-1)^(n+1). - Vaclav Kotesovec, Jun 23 2018
EXAMPLE
E.g.f.: A(x) = x + 4*x^2/2! + 22*x^3/3! + 155*x^4/4! + 1333*x^5/5! + 13541*x^6/6! + ...
MAPLE
H:= proc(n) H(n):= 1/n +`if`(n=1, 0, H(n-1)) end:
a:= n-> add(abs(Stirling1(n, k))*H(k)*k!, k=1..n):
seq(a(n), n=0..23); # Alois P. Heinz, Jun 21 2018
MATHEMATICA
nmax = 21; CoefficientList[Series[-Log[1 + Log[1 - x]]/(1 + Log[1 - x]), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[Abs[StirlingS1[n, k]] HarmonicNumber[k] k!, {k, 0, n}], {n, 0, 21}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jun 20 2018
STATUS
approved