A160447 - OEIS

%I #31 Apr 03 2020 17:03:52

%S 1,1,32,1393,336465,207388305,268749463729,645244638648481,

%T 2642912633259448386,17340131659334061379490,

%U 173401255467914281827442642,2538767439061885080225425717858,52643878634689290630033137748571475

%N Number of isomorphism classes of n-fold coverings of a connected graph with Betti number 5.

%C Number of orbits of the conjugacy action of Sym(n) on Sym(n)^5 [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="/A160447/b160447.txt">Table of n, a(n) for n = 0..60</a> [a(0)=1 prepended by _Georg Fischer_, Apr 03 2020]

%H J. H. Kwak and J. 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.

%o (Sage)

%o [sum(p.aut()**4 for p in Partitions(n)) for n in range(6)] # _Álvar Ibeas_, Mar 24 2015

%Y Sixth column of A160449.

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Nov 12 2009

%E Name clarified and more terms added by _Álvar Ibeas_, Mar 24 2015

%E a(0)=1 prepended by _F. Chapoton_, Mar 15 2020