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

1,5

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

Table of n, a(n) for n=1..49.

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.

Example

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 ...

Crossrefs

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

Sequence in context: A022166 A141689 A058669 * A059328 A174387 A176791

Adjacent sequences: A057001 A057002 A057003 * A057005 A057006 A057007

Keyword

nonn,tabl,nice

Author

N. J. A. Sloane, Sep 09 2000

Extensions

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

Status

approved