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A052502
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Number of permutations sigma without fixed point such that sigma^3=Id.
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10
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1, 2, 40, 2240, 246400, 44844800, 12197785600, 4635158528000, 2345390215168000, 1524503639859200000, 1237896955565670400000, 1227993779921145036800000, 1461312598106162593792000000, 2054605512937264606871552000000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| For n >= 1 a(n) is the size of the conjugacy class in the symmetric group S_(3n) consisting of permutations that their cycle decomposition is a product of n disjoint 3-cycles.
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 27
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FORMULA
| a(n) = (3*n)!/(n!*3^n). Using Stirling's formula in A000142 we have a(n) ~ sqrt(3) * 9^n * (n/e)^(2n). - Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 21 2001
Every third coefficient in the expansion of exp((x^3)/3).
G.f.: hypergeom([1/3, 2/3, 1], [], 9*x).
Recurrence: a(0) = 1, a(n) = (3*n-1)*(3*n-2)*a(n-1) for n >= 1.
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MAPLE
| spec := [S, {S=Set(Union(Cycle(Z, card=3)))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
| s=1; lst={s}; Do[s+=(s*=n)*n; AppendTo[lst, s], {n, 1, 5!, 3}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 15 2008]
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CROSSREFS
| Cf. A000142. Row sums of triangle A060063.
First column of array A091752 (also negative of second column).
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Mar 07 2009: (Start)
Equals row sums of A157702
(End)
Sequence in context: A000816 A000819 A060079 * A104134 A162868 A059476
Adjacent sequences: A052499 A052500 A052501 * A052503 A052504 A052505
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KEYWORD
| easy,nonn
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AUTHOR
| encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
| Edited by W. Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Feb 13 2004
A. K. Penson (penson_AT_ lptl_DOT_jussieu_DOT_fr) suggested that the row sums of A060063 coincide with this entry.
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