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A152612 Number of isomorphism classes of n-fold coverings of a connected graph with Betti number 3.

%I A152612 #42 May 05 2024 01:50:36
%S A152612 1,8,49,681,14721,524137,25471105,1628116890,131789656610,
%T A152612 13174980291658,1593894406662866,229496526010111571,
%U A152612 38782290669508033003,7600987633299112125995,1710169549495739472301076,437793904386312274903991653,126520458075485848061740557461
%N A152612 Number of isomorphism classes of n-fold coverings of a connected graph with Betti number 3.
%C A152612 Number of orbits of the conjugacy action of Sym(n) on Sym(n)^3 [Kwak and Lee, 2001]. - _Álvar Ibeas_, Mar 24 2015
%D A152612 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 A152612 Álvar Ibeas, <a href="/A152612/b152612.txt">Table of n, a(n) for n = 1..60</a>
%H A152612 Joseph Ben Geloun and Sanjaye Ramgoolam, <a href="https://doi.org/10.4171/aihpd/4">Counting Tensor Model Observables and Branched Covers of the 2-Sphere</a>, Annales de l'Institut Henri Poincaré D, Vol. 1, No. 1 (2014), pp. 77-138; <a href="https://arxiv.org/abs/1307.6490">arXiv preprint</a>, arXiv:1307.6490 [hep-th], 2013.
%H A152612 Jin Ho Kwak and Jaeun Lee, <a href="https://doi.org/10.4153/CJM-1990-039-3">Isomorphism classes of graph bundles</a>. Can. J. Math., 42(4), 1990, pp. 747-761.
%t A152612 A057006 = Import["https://oeis.org/A057006/b057006.txt", "Table"][[All, 2]];
%t A152612 etr[p_] := Module[{b}, b[n_] := b[n] = If[n == 0, 1, Sum[DivisorSum[j, # p[#]&] b[n - j], {j, 1, n}]/n]; b];
%t A152612 a = etr[A057006[[#]]&];
%t A152612 Array[a, 15] (* _Jean-François Alcover_, Aug 29 2019 *)
%o A152612 (Sage) [sum(p.aut()**2 for p in Partitions(n)) for n in range(1,8)] # _Álvar Ibeas_, Mar 24 2015
%Y A152612 Euler transform of A057006.
%Y A152612 Fourth column of A160449.
%K A152612 nonn
%O A152612 1,2
%A A152612 _N. J. A. Sloane_, Nov 12 2009
%E A152612 a(6) and a(7) from Geloun and Ramgoolan (2013) added by _N. J. A. Sloane_, Nov 21 2013
%E A152612 Name clarified and more terms added by _Álvar Ibeas_, Mar 24 2015