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A152612
Number of isomorphism classes of n-fold coverings of a connected graph with Betti number 3.
3
1, 8, 49, 681, 14721, 524137, 25471105, 1628116890, 131789656610, 13174980291658, 1593894406662866, 229496526010111571, 38782290669508033003, 7600987633299112125995, 1710169549495739472301076, 437793904386312274903991653, 126520458075485848061740557461
OFFSET
1,2
COMMENTS
Number of orbits of the conjugacy action of Sym(n) on Sym(n)^3 [Kwak and Lee, 2001]. - Álvar Ibeas, Mar 24 2015
REFERENCES
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.
LINKS
Joseph Ben Geloun and Sanjaye Ramgoolam, Counting Tensor Model Observables and Branched Covers of the 2-Sphere, Annales de l'Institut Henri Poincaré D, Vol. 1, No. 1 (2014), pp. 77-138; arXiv preprint, arXiv:1307.6490 [hep-th], 2013.
Jin Ho Kwak and Jaeun Lee, Isomorphism classes of graph bundles. Can. J. Math., 42(4), 1990, pp. 747-761.
MATHEMATICA
A057006 = Import["https://oeis.org/A057006/b057006.txt", "Table"][[All, 2]];
etr[p_] := Module[{b}, b[n_] := b[n] = If[n == 0, 1, Sum[DivisorSum[j, # p[#]&] b[n - j], {j, 1, n}]/n]; b];
a = etr[A057006[[#]]&];
Array[a, 15] (* Jean-François Alcover, Aug 29 2019 *)
PROG
(Sage) [sum(p.aut()**2 for p in Partitions(n)) for n in range(1, 8)] # Álvar Ibeas, Mar 24 2015
CROSSREFS
Euler transform of A057006.
Fourth column of A160449.
Sequence in context: A176626 A176674 A176694 * A298227 A298151 A299125
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 12 2009
EXTENSIONS
a(6) and a(7) from Geloun and Ramgoolan (2013) added by N. J. A. Sloane, Nov 21 2013
Name clarified and more terms added by Álvar Ibeas, Mar 24 2015
STATUS
approved