OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..451
FORMULA
a(n) = Sum_{k=1..n} Stirling1(n,k)*H(k)*k!, where H(k) is the k-th harmonic number.
EXAMPLE
E.g.f.: A(x) = x + 2*x^2/2! + 4*x^3/3! + 11*x^4/4! + 33*x^5/5! + 131*x^6/6! + ...
MAPLE
H:= proc(n) H(n):= 1/n +`if`(n=1, 0, H(n-1)) end:
a:= n-> add(Stirling1(n, k)*H(k)*k!, k=1..n):
seq(a(n), n=0..27); # Alois P. Heinz, Jun 21 2018
MATHEMATICA
nmax = 24; CoefficientList[Series[-Log[1 - Log[1 + x]]/(1 - Log[1 + x]), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[StirlingS1[n, k] HarmonicNumber[k] k!, {k, 0, n}], {n, 0, 24}]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Jun 20 2018
STATUS
approved