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Search: id:A027837
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| A027837 |
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Number of subgroups of index n in free group of rank 3. |
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+0
7
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| 1, 7, 97, 2143, 68641, 3011263, 173773153, 12785668351, 1169623688353, 130305512589247, 17376934722756577, 2733655173624167551, 501034099176714373921, 105847486567006696384831
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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M. Hall, Subgroups of finite index in free groups, Canad. J. Math., 1 (1949), 187-190.
P. de la Harpe, Topics in Geometric Group Theory, Univ. Chicago Press, 2000, p. 23.
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.
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.13(b).
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FORMULA
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a(n)=n*n!^2-Sum k!^2*a(n-k), k=1..n-1.
L.g.f.: Sum_{n>=1} a(n)*x^n/n = log( Sum_{n>=1} (n-1)!^2*x^n ). [From Paul D. Hanna (pauldhanna(AT)juno.com), Apr 13 2009]
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PROGRAM
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(PARI) {a(n)=n*polcoeff(log(sum(k=0, n, k!^2*x^k)+x*O(x^n)), n)} [From Paul D. Hanna (pauldhanna(AT)juno.com), Apr 13 2009]
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CROSSREFS
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Cf. A003319, A049290-A049295.
Sequence in context: A058805 A132061 A003710 this_sequence A046908 A005014 A157035
Adjacent sequences: A027834 A027835 A027836 this_sequence A027838 A027839 A027840
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KEYWORD
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easy,nice,nonn
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AUTHOR
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V. A. Liskovets (liskov(AT)im.bas-net.by)
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Oct 05 2000
Further terms from Naohiro Nomoto (6284968128(AT)geocities.co.jp), Jun 18 2001
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