OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Ayhan Dil and Veli Kurt, Polynomials related to harmonic numbers and evaluation of harmonic number series I, INTEGERS, 12 (2012), #A38.
FORMULA
a(n) = Sum_{k=0..n} Stirling2(n,k)*|Stirling1(k+1,2)|.
Maximal term in the sum is asymptotically in position k = n/(2*log(2)) and limit n-> infinity (a(n)/n!)^(1/n) = 1/log(2). - Vaclav Kotesovec, Feb 09 2013
E.g.f.: -log(2 - exp(x))/(2 - exp(x)). - Ilya Gutkovskiy, May 31 2018
a(n) ~ n! * log(n) / (2 * (log(2))^(n+1)) * (1 + (gamma - log(2) - log(log(2))) / log(n)), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Oct 13 2018
MATHEMATICA
Table[Sum[StirlingS2[n, k]*Abs[StirlingS1[k + 1, 2]], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Feb 09 2013 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Feb 08 2013
STATUS
approved