%I #25 Aug 06 2024 21:14:01
%S 3,12,84,876,12180,211692,4415124,107430636,2987482260,93461994732,
%T 3248794543764,124223034396396,5181679901192340,234153759187726572,
%U 11395053576644512404,594148263021558162156
%N "CIJ" (necklace, indistinct, labeled) transform of 3,3,3,3...
%H Christian G. Bower, <a href="/transforms2.html">Transforms (2)</a>
%H <a href="/index/Ne#necklaces">Index entries for sequences related to necklaces</a>
%F From _Vladeta Jovovic_, Sep 14 2003: (Start)
%F E.g.f.: -log(4-3*exp(x)).
%F a(n) = Sum_{k=1..n} 3^k*(k-1)!*Stirling2(n, k). (End)
%F a(n) ~ (n-1)! / (log(4/3))^n. - _Vaclav Kotesovec_, Mar 29 2014
%F a(n) = 3 * (1 + Sum_{k=1..n-1} binomial(n-1,k-1) * a(k)). - _Ilya Gutkovskiy_, Aug 09 2020
%t Table[ PolyLog[n, 3/4], {n, 0, -15, -1}] (* _Robert G. Wilson v_, Aug 05 2010 *)
%o (PARI) a(n)=polylog(1-n,3/4) \\ _Charles R Greathouse IV_, Aug 27 2014
%Y Cf. A000629, A027882.
%K nonn
%O 1,1
%A _Christian G. Bower_