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%I M4942 #35 Apr 13 2022 13:25:18
%S 0,1,14,130,700,2635,7826,19684,43800,88725,166870,295526,498004,
%T 804895,1255450,1899080,2796976,4023849,5669790,7842250,10668140,
%U 14296051,18898594,24674860,31853000,40692925,51489126,64573614
%N Number of ways to color vertices of a hexagon using <= n colors, allowing only rotations.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Victor Meally, <a href="/A006556/a006556.pdf">Letter to N. J. A. Sloane</a>, no date.
%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%F n*(n+1)*(n^2+n+1)*(n^2-2*n+2)/6.
%p A006565 := n-> (n^6+n^3+2*n^2+2*n)/6.
%p A006565:=-(1+7*z+53*z**2+49*z**3+10*z**4)/(z-1)**7; [Conjectured by _Simon Plouffe_ in his 1992 dissertation.]
%Y Cf. A027670, A075195.
%K nonn
%O 0,3
%A _N. J. A. Sloane_.
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