A032183 "CIJ" (necklace, indistinct, labeled) transform of 3,3,3,3...
3, 12, 84, 876, 12180, 211692, 4415124, 107430636, 2987482260, 93461994732, 3248794543764, 124223034396396, 5181679901192340, 234153759187726572, 11395053576644512404, 594148263021558162156
Offset: 1
Keywords
Links
- Christian G. Bower, Transforms (2)
- Index entries for sequences related to necklaces
Programs
-
Mathematica
Table[ PolyLog[n, 3/4], {n, 0, -15, -1}] (* Robert G. Wilson v, Aug 05 2010 *) -
PARI
a(n)=polylog(1-n,3/4) \\ Charles R Greathouse IV, Aug 27 2014
Formula
From Vladeta Jovovic, Sep 14 2003: (Start)
E.g.f.: -log(4-3*exp(x)).
a(n) = Sum_{k=1..n} 3^k*(k-1)!*Stirling2(n, k). (End)
a(n) ~ (n-1)! / (log(4/3))^n. - Vaclav Kotesovec, Mar 29 2014
a(n) = 3 * (1 + Sum_{k=1..n-1} binomial(n-1,k-1) * a(k)). - Ilya Gutkovskiy, Aug 09 2020