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A057004 Array T(n,k) = number of conjugacy classes of subgroups of index k in free group of rank n, read by antidiagonals. 11

%I

%S 1,1,1,1,3,1,1,7,7,1,1,15,41,26,1,1,31,235,604,97,1,1,63,1361,14120,

%T 13753,624,1,1,127,7987,334576,1712845,504243,4163,1,1,255,47321,

%U 7987616,207009649,371515454,24824785,34470,1,1,511,281995,191318464

%N Array T(n,k) = number of conjugacy classes of subgroups of index k in free group of rank n, read by antidiagonals.

%D M. Hofmeister, A Note on Counting Connected Graph Covering Projections, SIAM J. Discrete Math., 11 (1998), 286-292. See page 291 Table 4.3.

%D J. H. Kwak and J. Lee, J. Graph Th., 23 (1996), 105-109.

%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.

%D V. A. Liskovets, Reductive enumeration under mutually orthogonal group actions, Acta Applic. Math., 52 (1998), 91-120.

%D R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.13(c), pp. 76, 112.

%H J. H. Kwak and J. Lee, <a href="http://com2mac.postech.ac.kr/resorce/Lecture_text.htm">Enumeration of graph coverings and surface branched coverings</a>, Lecture Note Series 1 (2001), Com^2MaC-KOSEF, Korea. See chapter 3.

%e Array T(n,k) begins:

%e 1 1 1 1 1 1 1 ...

%e 1 3 7 26 97 624 4163 ...

%e 1 7 41 604 13753 504243 ...

%e 1 15 235 14120 1712845 ...

%Y Rows, columns, main diagonal give A057005-A057013, A160871.

%K nonn,tabl,nice

%O 1,5

%A _N. J. A. Sloane_, Sep 09 2000

%E More terms from Francisco Salinas (franciscodesalinas(AT)hotmail.com), Dec 25 2001

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Last modified July 19 08:23 EDT 2019. Contains 325155 sequences. (Running on oeis4.)