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%I #8 Nov 08 2017 17:18:42
%S 1,-1,2,-3,7,-11,17,-21,35,-67,125,-179,246,-384,715,-1199,1871,-2850,
%T 4593,-7589,12811,-20366,31545,-50483,84597,-138964,222534,-352910,
%U 569680,-931694,1523165,-2451150,3924137,-6331780,10329289,-16804843,27109912,-43594466,70485938,-114450985,185713588,-300089184,484106880,-782672321,1269075821,-2056723036,3325362211,-5371243069,8688055226
%N G.f.: 1 + Sum_{n=-oo..+oo, n<>0} (x - x^n)^n / (1 - (x - x^n)^n).
%C Compare g.f. to: Sum_{n=-oo..+oo} (x - x^(n+1))^n = 0.
%C Compare g.f. to: Sum_{n=-oo..+oo, n<>0} x^n/(1 - x^n) = 0, ignoring constant terms.
%C Limit a(n+1)/a(n) = -(sqrt(5) + 1)/2.
%H Paul D. Hanna, <a href="/A294677/b294677.txt">Table of n, a(n) for n = 0..300</a>
%F a(n) ~ (-1)^n * (1 + sqrt(5))^(n+1) / 2^(n+2). - _Vaclav Kotesovec_, Nov 08 2017
%e G.f.: A(x) = 1 - x + 2*x^2 - 3*x^3 + 7*x^4 - 11*x^5 + 17*x^6 - 21*x^7 + 35*x^8 - 67*x^9 + 125*x^10 - 179*x^11 + 246*x^12 - 384*x^13 + 715*x^14 - 1199*x^15 + 1871*x^16 - 2850*x^17 + 4593*x^18 - 7589*x^19 + 12811*x^20 - 20366*x^21 + 31545*x^22 - 50483*x^23 + 84597*x^24 - 138964*x^25 +...
%o (PARI) {a(n) = my(A); A = sum(m=-n-1,n+1, if(m==0,1, (x-x^m)^m/(1 - (x-x^m +x*O(x^n))^m ))); polcoeff(A,n)}
%o for(n=0,40,print1(a(n),", "))
%Y Cf. A290003.
%K sign
%O 0,3
%A _Paul D. Hanna_, Nov 07 2017
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