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

1, 8, 49, 681, 14721, 524137, 25471105, 1628116890, 131789656610, 13174980291658, 1593894406662866, 229496526010111571, 38782290669508033003, 7600987633299112125995, 1710169549495739472301076

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

Álvar Ibeas, Table of n, a(n) for n = 1..60

J. B. Geloun, S. Ramgoolam, Counting Tensor Model Observables and Branched Covers of the 2-Sphere, arXiv:1307.6490 [hep-th], 2013.

J. H. Kwak and J. 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

Adjacent sequences: A152609 A152610 A152611 * A152613 A152614 A152615

Keyword

nonn,more

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