%I #42 May 05 2024 01:50:36
%S 1,8,49,681,14721,524137,25471105,1628116890,131789656610,
%T 13174980291658,1593894406662866,229496526010111571,
%U 38782290669508033003,7600987633299112125995,1710169549495739472301076,437793904386312274903991653,126520458075485848061740557461
%N Number of isomorphism classes of n-fold coverings of a connected graph with Betti number 3.
%C Number of orbits of the conjugacy action of Sym(n) on Sym(n)^3 [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="/A152612/b152612.txt">Table of n, a(n) for n = 1..60</a>
%H 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 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 A057006 = Import["https://oeis.org/A057006/b057006.txt", "Table"][[All, 2]];
%t 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 a = etr[A057006[[#]]&];
%t Array[a, 15] (* _Jean-François Alcover_, Aug 29 2019 *)
%o (Sage) [sum(p.aut()**2 for p in Partitions(n)) for n in range(1,8)] # _Álvar Ibeas_, Mar 24 2015
%Y Euler transform of A057006.
%Y Fourth column of A160449.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Nov 12 2009
%E a(6) and a(7) from Geloun and Ramgoolan (2013) added by _N. J. A. Sloane_, Nov 21 2013
%E Name clarified and more terms added by _Álvar Ibeas_, Mar 24 2015