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Search: id:A065490
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| A065490 |
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Exponents in expansion of constant A065463 as Product_{n>1} zeta(n)^(-a(n)). |
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+0
2
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| 0, 1, -1, 1, -2, 3, -4, 5, -8, 13, -18, 25, -40, 62, -90, 135, -210, 324, -492, 750, -1164, 1809, -2786, 4305, -6710, 10460, -16264, 25350, -39650, 62057, -97108, 152145, -238818, 375165, -589520, 927200, -1459960, 2300346, -3626200
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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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.
Inverse Euler transform of F(1-n) where F() is Fibonacci numbers A000045. - Michael Somos, Jul 21 2003
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REFERENCES
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G. I. Lehrer and G. B. Segal, Homology stability for classical regular semisimple varieties, Math. Zeit., 236 (2001), 251-290.
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LINKS
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G. I. Lehrer, Some sequences arising at the interface of representation theory and homotopy theory
G. Niklasch, Some number theoretical constants: 1000-digit values
N. J. A. Sloane, Transforms
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FORMULA
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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
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PROGRAM
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(PARI) a(n)=if(n<1, 0, sumdiv(n, d, (-1)^d*moebius(n/d)*(fibonacci(d+1)+fibonacci(d-1)-1))/n)
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CROSSREFS
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Cf. A065463.
Adjacent sequences: A065487 A065488 A065489 this_sequence A065491 A065492 A065493
Sequence in context: A113439 A018059 A050024 this_sequence A051706 A162901 A162900
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KEYWORD
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sign
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Nov 19 2001
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EXTENSIONS
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More terms and formula from Christian G. Bower (bowerc(AT)usa.net), Aug 23 2002
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