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%I #13 Aug 10 2019 05:34:09
%S 1,97,13753,1712845,207009649,24875000437,2985789977353,
%T 358313458071085,42998059096839649,5159777705044971877,
%U 619173578774772949753,74300835546376264277725
%N Number of conjugacy classes of subgroups of index 5 in free group of rank n.
%D R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.13(c), pp. 76, 112.
%H J. H. Kwak and J. Lee, <a href="https://doi.org/10.1002/(SICI)1097-0118(199610)23:2<105::AID-JGT1>3.0.CO;2-X">Enumeration of connected graph coverings</a>, J. Graph Th., 23 (1996), 105-109.
%H J. H. Kwak and J. Lee, <a href="https://web.archive.org/web/20061002144237/http://com2mac.postech.ac.kr/Lecture/Lec-1.pdf">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, <a href="https://doi.org/10.1023/A:1005950823566">Reductive enumeration under mutually orthogonal group actions</a>, Acta Applic. Math., 52 (1998), 91-120.
%F 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)).
%F a(n) = 120^(n-1)-24^(n-1)-12^(n-1)+6^(n-1)+5^(n-1)+4^(n-1)-2^(n-1).
%o (PARI) a(n)=if(n<0,0,n--;120^n-24^n-12^n+6^n+5^n+4^n-2^n)
%Y Cf. A057004-A057013.
%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
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