%I #22 Sep 14 2021 01:00:26
%S 1,7,41,604,13753,504243,24824785,1598346352,129958211233,
%T 13030565312011,1579721338432537,227804599861102676,
%U 38541084552054952009,7560534755192908672087,1702288146755359962223409
%N Number of conjugacy classes of subgroups of index n in free group of rank 3.
%D R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.13(c), pp. 76, 112.
%H Vaclav Kotesovec, <a href="/A057006/b057006.txt">Table of n, a(n) for n = 1..60</a>
%H J. B. Geloun and S. Ramgoolam, <a href="http://arxiv.org/abs/1307.6490">Counting Tensor Model Observables and Branched Covers of the 2-Sphere</a>, arXiv preprint arXiv:1307.6490 [hep-th], 2013.
%H Joseph Ben Geloun and Sanjaye Ramgoolam, <a href="https://arxiv.org/abs/2106.01470">All-orders asymptotics of tensor model observables from symmetries of restricted partitions</a>, arXiv:2106.01470 [hep-th], 2021.
%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="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, <a href="https://doi.org/10.1023/A:1005950823566">Reductive enumeration under mutually orthogonal group actions</a>, Acta Applic. Math., 52 (1998), 91-120.
%H P. Vrana, <a href="https://doi.org/10.1088/1751-8113/44/22/225304">On the algebra of local unitary invariants of pure and mixed quantum states</a>, J. Phys A: Math. Theor. 44 (2011) 225304 doi:10.1088/1751-8113/44/22/225304, Table 2.
%Y Cf. A057004-A057013. Inverse Euler transform of A152612.
%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