This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A065490 #27 Apr 27 2023 06:29:56
%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
%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} V_k be the graded vector space H_*(PC^oo)[1], which has Poincaré series [or 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
%H A065490 Alois P. Heinz, <a href="/A065490/b065490.txt">Table of n, a(n) for n = 1..2000</a>
%H A065490 G. I. Lehrer, <a href="/A098787/a098787.pdf">Some sequences arising at the interface of representation theory and homotopy theory</a>
%H A065490 G. I. Lehrer and G. B. Segal, <a href="http://dx.doi.org/10.1007/PL00004831">Homology stability for classical regular semisimple varieties</a>, Math. Zeit., 236 (2001), 251-290.
%H A065490 G. Niklasch, <a href="/A001692/a001692.html">Some number theoretical constants: 1000-digit values</a> [Cached copy]
%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_, May 03 2003
%F A065490 a(n) ~ (-1)^n * phi^n / n, where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - _Vaclav Kotesovec_, Oct 09 2019
%t A065490 a[n_] := DivisorSum[n, (-1)^#*MoebiusMu[n/#]*(Fibonacci[#+1] + Fibonacci[# -1]-1)&]/n; Array[a, 40] (* _Jean-François Alcover_, Dec 03 2015, adapted from PARI *)
%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.
%K A065490 sign
%O A065490 1,5
%A A065490 _N. J. A. Sloane_, Nov 19 2001
%E A065490 More terms and formula from _Christian G. Bower_, Aug 23 2002