%I A005225 M0903
%S A005225 1,2,3,10,25,176,721,6406,42561,436402,3628801,48073796,479001601,
%T A005225 7116730336,88966701825,1474541093026,20922789888001,400160588853026,
%U A005225 6402373705728001,133991603578884052,2457732174030848001
%N A005225 Number of permutations of length n with equal cycles.
%C A005225 a(n)=(n-1)!+1 iff n is a prime.
%D A005225 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005225 D. P. Walsh, A differentiation-based characterization of primes, Abstracts 
               Amer. Math. Soc., 25 (No. 2, 2002), p. 339, #975-11-237.
%D A005225 H. S. Wilf, Three problems in combinatorial asymptotics, J. Combin. Theory, 
               A 35 (1983), 199-207.
%H A005225 D. P. Walsh, <a href="http://www.mtsu.edu/~dwalsh/primetst.html">Primality 
               test based on the generating function</a>
%H A005225 D. P. Walsh, <a href="http://www.mtsu.edu/~dwalsh/primech.html">A differentiation-based 
               characterization of primes</a>
%F A005225 a(n) = n!*sum(((n/k)!*k^(n/k))^(-1)) where sum is over all divisors k 
               of n. Exponential generating function [for a(1) through a(n)]= sum(exp(t^k/
               k), k=1..n).
%e A005225 For example, a(4)=10 since, of the 24 permutations of length 4, there 
               are 6 permutations with consist of a single 4-cycle, 3 permutations 
               that consist of two 2-cycles and 1 permutation with four 1-cycles. 
               Also, a(7)=721 since there are 720 permutations with a single cycle 
               of length 7 and 1 permutation with seven 1-cycles.
%Y A005225 Sequence in context: A123029 A103018 A005158 this_sequence A052929 A151415 
               A134588
%Y A005225 Adjacent sequences: A005222 A005223 A005224 this_sequence A005226 A005227 
               A005228
%K A005225 nonn,easy,nice
%O A005225 1,2
%A A005225 N. J. A. Sloane (njas(AT)research.att.com).
%E A005225 Additional comments from Dennis P. Walsh (dwalsh(AT)mtsu.edu), Dec 08 
               2000
%E A005225 More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 01 2001