Search: id:A001189
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%I A001189 M2801 N1127
%S A001189 0,1,3,9,25,75,231,763,2619,9495,35695,140151,568503,2390479,10349535,
%T A001189 46206735,211799311,997313823,4809701439,23758664095,119952692895,
%U A001189 618884638911,3257843882623,17492190577599,95680443760575
%N A001189 Number of degree-n permutations of order exactly 2.
%C A001189 Number of set partitions of [n] into blocks of size 2 and 1 with at least 
               one block of size 2. - Olivier GERARD (olivier.gerard(AT)gmail.com), 
               Oct 29 2007
%D A001189 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001189 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001189 R. B. Herrera, The number of elements of given period in finite symmetric 
               group, Amer. Math. Monthly 64, 1957, 488-490.
%D A001189 L. Moser and M. Wyman, On solutions of x^d = 1 in symmetric groups, Canad. 
               J. Math., 7 (1955), 159-168.
%D A001189 Thanatipanonda, Thotsaporn, Inversions and major index for permutations, 
               Math. Mag., No. 4, 2004
%F A001189 a(n) = b(n, 2), where b(n, d)=Sum_{k=1..n} (n-1)!/(n-k)! * Sum_{l:lcm{k, 
               l}=d} b(n-k, l), b(0, 1)=1 is the number of degree-n permutations 
               of order exactly d.
%F A001189 E.g.f.: -exp(x)+exp(x+1/2*x^2).
%F A001189 a(n) = a(n-1)+(1+a(n-2))*(n-1) = Sum_{j = 1 to floor[n/2]}[n!/(j!*(n-2j)!*(2^j))] 
               = A000085(n)-1. - Henry Bottomley (se16(AT)btinternet.com), May 03 
               2001
%Y A001189 Equals A000085 - 1. Cf. A001470 - A001473, A052501, A053496-A053504, 
               A061121-A061128.
%Y A001189 Sequence in context: A101499 A004665 A132835 this_sequence A101786 A012771 
               A120284
%Y A001189 Adjacent sequences: A001186 A001187 A001188 this_sequence A001190 A001191 
               A001192
%K A001189 nonn,nice,easy
%O A001189 1,3
%A A001189 N. J. A. Sloane (njas(AT)research.att.com).
%E A001189 More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 14 2001

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