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

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, 13753, 624, 1, 1, 127, 7987, 334576, 1712845, 504243, 4163, 1, 1, 255, 47321, 7987616, 207009649, 371515454, 24824785, 34470, 1, 1, 511, 281995, 191318464

Offset: 1

Author

N. J. A. Sloane, Sep 09 2000

Keywords

• nonn
• tabl
• nice

Examples

			Array T(n,k) begins:
1 1 1 1 1 1 1 ...
1 3 7 26 97 624 4163 ...
1 7 41 604 13753 504243 ...
1 15 235 14120 1712845 ...
		

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

Links

• M. Hofmeister, A Note on Counting Connected Graph Covering Projections, SIAM J. Discrete Math., 11 (1998), 286-292. See page 291 Table 4.3.
• J. H. Kwak and J. Lee, Enumeration of connected graph coverings, J. Graph Th., 23 (1996), 105-109.
• J. H. Kwak and J. Lee, Enumeration of graph coverings and surface branched coverings, Lecture Note Series 1 (2001), Com^2MaC-KOSEF, Korea. See chapter 3.
• V. A. Liskovets, Reductive enumeration under mutually orthogonal group actions, Acta Applic. Math., 52 (1998), 91-120.

Crossrefs

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

Extensions

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