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%I #6 Dec 24 2017 16:07:08
%S 1,513,701260,1273147785,2597337494136,5711975829039480,
%T 13239412829570653440,31902976888441563215025,
%U 79210992511055955027177700,201394898991255834414075013488,522024491776928458970588283023040,1374924298868439440732405164346591160,3670434093979203432106449568933449100800,9911788665178411118992936004423729374579200
%N Number of configurations, excluding reflections and color swaps, of n beads each of five colors on a string.
%C Power Group Enumeration applies here.
%D E. Palmer and F. Harary, Graphical Enumeration, Academic Press, 1973.
%H Marko Riedel et al., <a href="https://math.stackexchange.com/questions/2530872/">Unique rows of pebbles</a>
%F With Z(S_{q,|m}) = [w^q] exp(Sum_{d|m} a_d w^d/d) and parameters n,k we have for nk even, (1/2) ((nk!)/k!/n!^k + (nk/2)! 2^(nk/2) [a_2^(nk/2)] Z(S_{k,|2})(Z_{n,|2}, a_2^n/n!) and for nk odd, (1/2) ((nk!)/k!/n!^k + ((nk-1)/2)! 2^((nk-1)/2) [a_1 a_2^((nk-1)/2)] Z(S_{k,|2})(Z_{n,|2}, a_2^n/n!). This sequence has k=5.
%Y Cf. A045723, A296143, A296144, A296146.
%K nonn
%O 1,2
%A _Marko Riedel_, Dec 05 2017
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