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Search: id:A057005
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| A057005 |
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Number of conjugacy classes of subgroups of index n in free group of rank 2. |
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+0
3
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| 1, 3, 7, 26, 97, 624, 4163, 34470, 314493, 3202839, 35704007, 433460014, 5687955737, 80257406982, 1211781910755, 19496955286194, 333041104402877, 6019770408287089, 114794574818830735, 2303332664693034476
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Number of (unlabeled) dessins d'enfants with n edges. A dessin d'enfant ("child's drawing") by A. Grothendieck, 1984, is a connected bipartite multigraph with properly bicolored nodes (w and b) in which a cyclic order of the incident edges is assigned to every node. For n=2 these are w--b--w, b--w--b and w==b. - Valery A. Liskovets (liskov(AT)im.bas-net.by), Mar 17 2005
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REFERENCES
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J. H. Kwak and J. Lee, J. Graph Th., 23 (1996), 105-109.
V. A. Liskovets, Reductive enumeration under mutually orthogonal group actions, Acta Applic. Math., 52 (1998), 91-120.
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.13(c), pp. 76, 112.
L. Zapponi, What is a dessin d'enfant?, Notices AMS, 50:7, 2003, 788-789.
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LINKS
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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.
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FORMULA
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prod_{n>0}(1-x^n)^{-a(n)}=prod_{i>0}sum_{j>=0}j!i^jx^{ij}. (Liskovets) - Valery A. Liskovets (liskov(AT)im.bas-net.by), Mar 17 2005
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CROSSREFS
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Cf. A057004-A057013.
Adjacent sequences: A057002 A057003 A057004 this_sequence A057006 A057007 A057008
Sequence in context: A057124 A038237 A069738 this_sequence A108217 A120120 A126472
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KEYWORD
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nonn
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AUTHOR
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njas, Sep 09 2000
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EXTENSIONS
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More terms from Francisco Salinas (franciscodesalinas(AT)hotmail.com), Dec 25 2001
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