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%I #27 Jul 12 2018 06:10:20
%S 2,6,30,222,2190,27006,399630,6899262,136125390,3021538686,
%T 74520313230,2021686771902,59833117024590,1918366107872766,
%U 66237821635330830,2450438532592334142,96696400596369539790
%N a(n) = sum_{k>=1} k^n (2/3)^k.
%H C. G. Bower, <a href="/transforms2.html">Transforms</a>
%H Steffen Greenfield, <a href="http://math.rutgers.edu/~greenfie/oldcourses/192/site/gifstuff/notes/sums-6.html">Source</a>
%H <a href="/index/Ne#necklaces">Index entries for sequences related to necklaces</a>
%F Also "CIJ" (necklace, indistinct, labeled) transform of 2, 2, 2, 2...
%F E.g.f. (for offset 1): -log(3-2*exp(x)). Sum_{k=1..n) 2^k*(k-1)!*Stirling2(n, k). - _Vladeta Jovovic_, Sep 14 2003
%F a(n) ~ n! / (log(3/2))^(n+1). - _Vaclav Kotesovec_, Oct 07 2013
%t Table[ PolyLog[n, 2/3], {n, 0, -18, -1}] (* _Robert G. Wilson v_, Aug 05 2010 *)
%t Table[Sum[StirlingS2[n, k] * (k-1)! * 2^k, {k, 1, n}], {n, 1, 20}] (* _Vaclav Kotesovec_, Jul 12 2018 *)
%o (PARI) a(n)=polylog(-n,2/3) \\ _Charles R Greathouse IV_, Aug 27 2014
%Y Cf. A000629, A032183.
%K nonn
%O 0,1
%A Stephen J. Greenfield (greenfie(AT)math.rutgers.edu)
%E More terms from _Christian G. Bower_
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