OFFSET
2,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 2..418
FORMULA
a(n) = Sum_{k=2..n} |Stirling1(n, k) * Stirling1(k, 2)|.
a(n) = Sum_{k=2..n} |Stirling1(n, k)| * (k-1)! * H(k-1), where H(k) is the k-th harmonic number.
a(n) = A052822(n) / 2.
a(n) ~ sqrt(2*Pi) * log(n) * n^(n - 1/2) / (exp(1) - 1)^n * (1 + (gamma - log(exp(1) - 1))/log(n)), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Feb 15 2021
MATHEMATICA
nmax = 22; 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, 22}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 15 2021
STATUS
approved