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Search: id:A052504
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| A052504 |
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Number of permutations sigma without fixed point such that sigma^5=Id. |
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+0
1
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OFFSET
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0,2
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COMMENT
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For n >= 1 a(n) is the size of the conjugacy class in the symmetric group S_(5n) consisting of permutations that their cycle decomposition is a product of n disjoint 5-cycles.
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LINKS
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INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 29
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FORMULA
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E.g.f.: exp(1/5*x^5)
a(n) = (5n)! / (n! * 5^n); a(0) = 1, a(1) = 24, for n >= 2 a(n) = a(n-1) * C(5n - 1, 4)* 24 = a(n-1)*(5n-1)*(5n-2)*(5n-3)*(5n-4); a(n) ~ sqrt(5) * 625^n * (n/e)^(4n). - Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 21 2001
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MAPLE
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spec := [S, {S=Set(Union(Cycle(Z, card=5)))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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CROSSREFS
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Adjacent sequences: A052501 A052502 A052503 this_sequence A052505 A052506 A052507
Sequence in context: A100733 A125048 A003920 this_sequence A061527 A056947 A048057
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KEYWORD
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easy,nonn
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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