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A049291
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Number of subgroups of index n in free group of rank 4.
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1
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1, 15, 625, 54335, 8563601, 2228419359, 893451975473, 523337983164799, 429463651385469649, 477364501208149290975, 699086688951391180496497, 1318072723102023442664430143, 3137514636520304660660007679505
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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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LINKS
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Table of n, a(n) for n=1..13.
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FORMULA
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a(n)=n*n!^3-Sum k!^3*a(n-k), k=1..n-1.
L.g.f.: Sum_{n>=1} a(n)*x^n/n = log( Sum_{n>=1} (n-1)!^3*x^n ). [From Paul D. Hanna, Apr 13 2009]
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MATHEMATICA
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ClearAll[a]; a[n_] := a[n] = n*n!^3 - Sum [k!^3*a[n - k], {k, 1, n - 1}]; Table[a[n], {n, 1, 13}] (* Jean-François Alcover, Oct 08 2012, from first formula *)
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PROG
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(PARI) {a(n)=n*polcoeff(log(sum(k=0, n, k!^3*x^k)+x*O(x^n)), n)} [From Paul D. Hanna, Apr 13 2009]
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CROSSREFS
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Cf. A003319, A027837, A049290-A049295.
Sequence in context: A012210 A203172 A081022 * A092958 A222268 A223203
Adjacent sequences: A049288 A049289 A049290 * A049292 A049293 A049294
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KEYWORD
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easy,nice,nonn
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AUTHOR
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Valery A. Liskovets
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EXTENSIONS
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More terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jun 17 2001
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STATUS
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approved
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