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%I #26 Apr 08 2016 12:06:42
%S 1,7,161,14721,1730861,207388305,24883501301,2985987361161,
%T 358318118583341,42998170050574305,5159780357316368741,
%U 619173642303122852601,74300837069552376921821,8916100448264989434407505,1069932053790827570370392981
%N Number of isomorphism classes of 5-fold coverings of a connected graph with Betti number n.
%C Number of orbits of the conjugacy action of Sym(5) on Sym(5)^n [Kwak and Lee, 2001]. - _Álvar Ibeas_, Mar 24 2015
%D J. H. Kwak and J. Lee, Enumeration of graph coverings, surface branched coverings and related group theory, in Combinatorial and Computational Mathematics (Pohang, 2000), ed. S. Hong et al., World Scientific, Singapore 2001, pp. 97-161.
%H Álvar Ibeas, <a href="/A160454/b160454.txt">Table of n, a(n) for n = 0..450</a>
%H M. W. Hero and J. F. Willenbring, <a href="http://dx.doi.org/10.1016/j.disc.2009.06.021">Stable Hilbert series as related to the measurement of quantum entanglement</a>, Discrete Math., 309 (2010), 6508-6514.
%H J. H. Kwak and J. Lee, <a href="http://cms.math.ca/cjm/v42/cjm1990v42.0747-0761.pdf">Isomorphism classes of graph bundles</a>. Can. J. Math., 42(4), 1990, pp. 747-761.
%H A. Prasad, <a href="http://arxiv.org/abs/1407.5284">Equivalence classes of nodes in trees and rational generating functions</a>, arXiv preprint arXiv:1407.5284 [math.CO], 2014.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (155,-4670,59440,-374304,1152000,-1382400).
%F a(n+1) = 4^n + 5^n + 2 * 6^n + 8^n + 12^n + 120^n. - _Álvar Ibeas_, Mar 24 2015
%F G.f.: -(249792*x^5-159200*x^4+36984*x^3-3746*x^2+148*x-1) / ((4*x-1)*(5*x-1)*(6*x-1)*(8*x-1)*(12*x-1)*(120*x-1)). - _Colin Barker_, Mar 24 2015
%t LinearRecurrence[{155,-4670,59440,-374304,1152000,-1382400},{1,7,161,14721,1730861,207388305},20] (* _Harvey P. Dale_, Apr 08 2016 *)
%o (PARI) Vec(-(249792*x^5-159200*x^4+36984*x^3-3746*x^2+148*x-1) / ((4*x-1)*(5*x-1)*(6*x-1)*(8*x-1)*(12*x-1)*(120*x-1)) + O(x^100)) \\ _Colin Barker_, Mar 24 2015
%Y Fifth row of A160449.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Nov 15 2009
%E Name clarified and more terms added by _Álvar Ibeas_, Mar 24 2015