Search: id:A059867
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%I A059867
%S A059867 1,2,2,4,4,8,8,8,8,16,16,32,32,64,64,16,16,32,32,64,64,128,128,128,128,
%T A059867 256,256,512,512,1024,1024,32,32,64,64,128,128,256,256,256,256,512,512,
%U A059867 1024,1024,2048,2048,512,512,1024,1024,2048,2048,4096,4096,4096,4096
%N A059867 Number of irreducible representations of the symmetric group S_n that 
               have odd degree.
%D A059867 John McKay, Irreducible representations of odd degree, Journal of Algebra 
               20, 1972 pages 416-418.
%F A059867 If n = sum 2^e[i] in binary, then the number of odd degree irreducible 
               complex representations of S_n is 2^sum e[i]. In words: write n in 
               binary and take the product of the powers of 2 that appear.
%F A059867 G.f.: prod(k>=0, 1 + 2^k * x^2^k). a(n) = 2^A073642(n). - Ralf Stephan, 
               Jun 02 2003
%F A059867 a(1)=1, a(2n) = 2^e1(n)*a(n), a(2n+1) = a(2n), where e1(n) = A000120(n). 
               - Ralf Stephan, Jun 19 2003
%e A059867 a(3) = 2 because S_3 the degrees of the irreducible representations of 
               S_3 are 1,1,2.
%Y A059867 Cf. A029930, A029931, A073642.
%Y A059867 Sequence in context: A138219 A100835 A120541 this_sequence A046971 A051754 
               A108747
%Y A059867 Adjacent sequences: A059864 A059865 A059866 this_sequence A059868 A059869 
               A059870
%K A059867 nonn,easy
%O A059867 1,2
%A A059867 Noam Katz (noamkj(AT)hotmail.com), Feb 28 2001
%E A059867 More terms from Larry Reeves (larryr(AT)acm.org), Mar 27 2001

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