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%I #35 Jan 30 2020 21:29:14
%S 3,9,54,486,5832,87480,1574640,33067440,793618560,21427701120,
%T 642831033600,21213424108800,763683267916800,29783647448755200,
%U 1250913192847718400,56291093678147328000,2701972496551071744000,137800597324104658944000,7441232255501651582976000
%N Number of necklaces with n labeled beads of 3 colors.
%H C. G. Bower, <a href="/transforms2.html">Transforms (2)</a>
%H Alexsandar Petojevic, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL5/Petojevic/petojevic5.html">The Function vM_m(s; a; z) and Some Well-Known Sequences</a>, Journal of Integer Sequences, Vol. 5 (2002), Article 02.1.7
%H <a href="/index/Ne#necklaces">Index entries for sequences related to necklaces</a>
%F "CIJ" (necklace, indistinct, labeled) transform of 3, 0, 0, 0...
%F E.g.f.: log(1/(1-3*x)).
%F a(n) = 3^n * (n-1)!. - _Vaclav Kotesovec_, Jan 05 2014
%F D-finite with recurrence: a(n) +3*(-n+1)*a(n-1)=0. - _R. J. Mathar_, Jan 28 2020
%t s=3; lst={s}; Do[s+=n*s+s; AppendTo[lst, s], {n, 1, 5!, 3}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 08 2008 *)
%t Rest[With[{nn=20}, CoefficientList[Series[Log[1/(1-3x)], {x,0,nn}], x] Range[0,nn]!]] (* _Harvey P. Dale_, Sep 22 2011 *)
%o (PARI) Vec(serlaplace(log(1/(1-3*'x+O('x^66))))) /* _Joerg Arndt_, Jan 25 2013 */
%K nonn,easy
%O 1,1
%A _Christian G. Bower_