OFFSET
2,3
FORMULA
a(n) = Sum_{k=2..n} |Stirling1(n, k)| * Stirling1(k, 2).
a(n) = (-1)^n * Sum_{k=2..n} Stirling1(n, k) * (k-1)! * H(k-1), where H(k) is the k-th harmonic number.
MATHEMATICA
nmax = 24; CoefficientList[Series[Log[1 - Log[1 - x]]^2/2, {x, 0, nmax}], x] Range[0, nmax]! // Drop[#, 2] &
Table[Sum[Abs[StirlingS1[n, k]] StirlingS1[k, 2], {k, 2, n}], {n, 2, 24}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 15 2021
STATUS
approved