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%I #10 Aug 30 2019 05:28:52
%S 1,3,97,54335,1035045121,1160799620549247,114730150164000898447873,
%T 1385904943637483363530115691960319,
%U 2706118201409447403878672281480056877837885441,1091106883064604841286281006789753438364086962298324514658303
%N Number of subgroups of index n in free group of rank n.
%D P. de la Harpe, Topics in Geometric Group Theory, Univ. Chicago Press, 2000, p. 23.
%D R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.13(b).
%H J. H. Kwak and J. Lee, <a href="http://com2mac.postech.ac.kr/resorce/Lecture_text.htm">Enumeration of graph coverings and surface branched coverings</a>, Lecture Note Series 1 (2001), Com^2MaC-KOSEF, Korea. See chapter 3.
%H V. A. Liskovets and A. Mednykh, <a href="https://doi.org/10.1080/00927870008826924">Enumeration of subgroups in the fundamental groups of orientable circle bundles over surfaces</a>, Commun. in Algebra, 28, No. 4 (2000), 1717-1738.
%t t[n_, k_] := t[n, k] = k*k!^(n - 1) - Sum[j!^(n - 1)*t[n, k - j], {j, 1, k - 1}];
%t a[n_] := t[n, n];
%t Array[a, 10] (* _Jean-François Alcover_, Aug 30 2019, after _Alois P. Heinz_ in A049290 *)
%Y Main diagonal of A049290.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Sep 09 2000
%E More terms from Francisco Salinas (franciscodesalinas(AT)hotmail.com), Dec 25 2001
%E a(10) from _Jean-François Alcover_, Aug 30 2019
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