A057011 Number of conjugacy classes of subgroups of index 5 in free group of rank n.

1, 97, 13753, 1712845, 207009649, 24875000437, 2985789977353, 358313458071085, 42998059096839649, 5159777705044971877, 619173578774772949753, 74300835546376264277725

Offset

1,2

References

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..12.

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.

Formula

G.f.: x(1-76x+4336x^2-81504x^3+522720x^4-1064448x^5)/((1-2x)(1-4x)(1-5x)(1-6x)(1-12x)(1-24x)(1-120x)).

a(n) = 120^(n-1)-24^(n-1)-12^(n-1)+6^(n-1)+5^(n-1)+4^(n-1)-2^(n-1).

Prog

(PARI) a(n)=if(n<0, 0, n--; 120^n-24^n-12^n+6^n+5^n+4^n-2^n)

Crossrefs

Cf. A057004-A057013.

Sequence in context: A189341 A189777 A302330 * A218591 A218205 A218232

Adjacent sequences: A057008 A057009 A057010 * A057012 A057013 A057014

Keyword

nonn

Author

N. J. A. Sloane, Sep 09 2000

Extensions

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

Status

approved