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A057011
Number of conjugacy classes of subgroups of index 5 in free group of rank n.
1
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
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
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