OFFSET
0,4
FORMULA
Sum_{n>=0} a(n) * x^n / n!^2 = Sum_{n>=1} H(n) * log(1+x)^n / n!.
MATHEMATICA
Table[n! Sum[StirlingS1[n, k] HarmonicNumber[k], {k, 1, n}], {n, 0, 17}]
nmax = 17; CoefficientList[Series[Sum[HarmonicNumber[k] Log[1 + x]^k/k!, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!^2
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Jun 03 2022
STATUS
approved