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%I #36 Feb 06 2017 16:32:54
%S 1,5,43,681,14491,336465,7997683,191374041,4588603531,110092229025,
%T 2641942301923,63404456863401,1521689741669371,36520416189619185,
%U 876488888356983763,21035724521756752761,504857318142580028011,12116575072428716250945,290797797234516859979203,6979147097598917713826121
%N Expansion of (1-34*x+276*x^2-584*x^3)/((1-3*x)*(1-4*x)*(1-8*x)*(1-24*x)).
%C Number of isomorphism classes of 4-fold coverings of a connected graph with Betti number n. [Kwak and Lee]
%C Number of orbits of the conjugacy action of Sym(4) on Sym(4)^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="/A160450/b160450.txt">Table of n, a(n) for n = 0..500</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_04">Index entries for linear recurrences with constant coefficients</a>, signature (39,-428,1728,-2304).
%F G.f.: (1-34*x+276*x^2-584*x^3)/((1-3*x)*(1-4*x)*(1-8*x)*(1-24*x)).
%F a(n) = 3^(n-1) + 2*4^(n-1) + 8^(n-1) + 24^(n-1). - _Álvar Ibeas_, Mar 24 2015
%t Table[3^(n - 1) + 2*4^(n - 1) + 8^(n - 1) + 24^(n - 1), {n, 0, 19}] (* _Michael De Vlieger_, Mar 24 2015 *)
%t LinearRecurrence[{39,-428,1728,-2304},{1,5,43,681},20] (* _Harvey P. Dale_, Feb 06 2017 *)
%o (PARI) Vec((1-34*x+276*x^2-584*x^3)/((1-3*x)*(1-4*x)*(1-8*x)*(1-24*x)) + O(x^30)) \\ _Michel Marcus_, Jan 14 2016
%Y Fourth row of A160449.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Nov 15 2009
%E Entry revised by _N. J. A. Sloane_, Sep 15 2014
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