Search: id:A065490
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%I A065490
%S A065490 0,1,1,1,2,3,4,5,8,13,18,25,40,62,90,135,210,324,492,750,
%T A065490 1164,1809,2786,4305,6710,10460,16264,25350,39650,62057,97108,
%U A065490 152145,238818,375165,589520,927200,1459960,2300346,3626200
%V A065490 0,1,-1,1,-2,3,-4,5,-8,13,-18,25,-40,62,-90,135,-210,324,-492,750,
%W A065490 -1164,1809,-2786,4305,-6710,10460,-16264,25350,-39650,62057,-97108,
%X A065490 152145,-238818,375165,-589520,927200,-1459960,2300346,-3626200
%N A065490 Exponents in expansion of constant A065463 as Product_{n>1} zeta(n)^(-a(n)).
%C A065490 The sequence 1,1,1,1,2,3,4,5,8,13,18,25,40,62,90,135,... appears in Lehrer-Segal 
               on p. 285, in the following context: Let V=Sum_{k=1..infty} V_k be 
               the graded vector space H_*(PC^infty)[1], which has Poincare series 
               p(t)=t/(1-t^2). This sequence gives the dimensions of the free graded 
               Lie algebra L on V.
%C A065490 Inverse Euler transform of F(1-n) where F() is Fibonacci numbers A000045. 
               - Michael Somos, Jul 21 2003
%D A065490 G. I. Lehrer and G. B. Segal, Homology stability for classical regular 
               semisimple varieties, Math. Zeit., 236 (2001), 251-290.
%H A065490 G. I. Lehrer, <a href="a098787.pdf">Some sequences arising at the interface 
               of representation theory and homotopy theory</a>
%H A065490 G. Niklasch, <a href="http://www.gn-50uma.de/alula/essays/Moree/Moree.en.shtml">
               Some number theoretical constants: 1000-digit values</a>
%H A065490 N. J. A. Sloane, <a href="transforms.txt">Transforms</a>
%F A065490 a(n) = (1/n)*Sum_{d|n} (-1)^d*mu(n/d)*(Fibonacci(d-1)+Fibonacci(d+1)-1). 
               - Vladeta Jovovic (vladeta(AT)eunet.rs), May 03 2003
%o A065490 (PARI) a(n)=if(n<1,0,sumdiv(n,d,(-1)^d*moebius(n/d)*(fibonacci(d+1)+fibonacci(d-1)-1))/
               n)
%Y A065490 Cf. A065463.
%Y A065490 Sequence in context: A113439 A018059 A050024 this_sequence A051706 A152526 
               A162901
%Y A065490 Adjacent sequences: A065487 A065488 A065489 this_sequence A065491 A065492 
               A065493
%K A065490 sign
%O A065490 1,5
%A A065490 N. J. A. Sloane (njas(AT)research.att.com), Nov 19 2001
%E A065490 More terms and formula from Christian G. Bower (bowerc(AT)usa.net), Aug 
               23 2002

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