A057014 Number of subgroups of index n in free group of rank n.

1, 3, 97, 54335, 1035045121, 1160799620549247, 114730150164000898447873, 1385904943637483363530115691960319, 2706118201409447403878672281480056877837885441, 1091106883064604841286281006789753438364086962298324514658303

Offset: 1

Author

N. J. A. Sloane, Sep 09 2000

Keywords

• nonn

References

• P. de la Harpe, Topics in Geometric Group Theory, Univ. Chicago Press, 2000, p. 23.
• R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.13(b).

Links

• 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 and A. Mednykh, Enumeration of subgroups in the fundamental groups of orientable circle bundles over surfaces, Commun. in Algebra, 28, No. 4 (2000), 1717-1738.

Crossrefs

Main diagonal of A049290.

Programs

Mathematica

t[n_, k_] := t[n, k] = k*k!^(n - 1) - Sum[j!^(n - 1)*t[n, k - j], {j, 1, k - 1}];
a[n_] := t[n, n];
Array[a, 10] (* Jean-François Alcover, Aug 30 2019, after Alois P. Heinz in A049290 *)

Extensions

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

a(10) from Jean-François Alcover, Aug 30 2019