Search: id:A052504
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%I A052504
%S A052504 1,24,72576,1743565824,162193467211776
%N A052504 Number of permutations sigma without fixed point such that sigma^5=Id.
%C A052504 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.
%H A052504 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=29">
               Encyclopedia of Combinatorial Structures 29</a>
%F A052504 E.g.f.: exp(1/5*x^5)
%F A052504 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
%p A052504 spec := [S,{S=Set(Union(Cycle(Z,card=5)))},labeled]: seq(combstruct[count](spec,
               size=n), n=0..20);
%Y A052504 Sequence in context: A158664 A125048 A003920 this_sequence A159388 A061527 
               A056947
%Y A052504 Adjacent sequences: A052501 A052502 A052503 this_sequence A052505 A052506 
               A052507
%K A052504 easy,nonn
%O A052504 0,2
%A A052504 encyclopedia(AT)pommard.inria.fr, Jan 25 2000

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