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%I #10 Aug 31 2013 00:44:14
%S 1,1,-3,14,-76,441,-2678,16813,-108093,707451,-4696017,31530792,
%T -213715953,1460072247,-10042361784,69473047716,-483046768116,
%U 3373552141194,-23653214175084,166422650191122,-1174621198245837,8314055808436788,-58998774106863513
%N G.f. A(x) satisfies: A(x)^8 = A(x^2)^4 + 8*x.
%C The limit a(n+1)/a(n) seems to be near -7.46...
%H Paul D. Hanna, <a href="/A223026/b223026.txt">Table of n, a(n) for n = 0..300</a>
%F Self-convolution yields A228711.
%e G.f.: A(x) = 1 + x - 3*x^2 + 14*x^3 - 76*x^4 + 441*x^5 - 2678*x^6 +-...
%e where
%e A(x)^8 = 1 + 8*x + 4*x^2 - 6*x^4 + 24*x^6 - 117*x^8 + 612*x^10 - 3426*x^12 +-...
%e A(x^2)^4 = 1 + 4*x^2 - 6*x^4 + 24*x^6 - 117*x^8 + 612*x^10 - 3426*x^12 +-...
%e A(x)^2 = 1 + 2*x - 5*x^2 + 22*x^3 - 115*x^4 + 646*x^5 - 3822*x^6 +-...
%o (PARI) {a(n)=local(A=1+x); for(i=1, #binary(n), A=(subst(A, x, x^2)^4+8*x+x*O(x^n))^(1/8)); polcoeff(A, n, x)}
%o for(n=0, 20, print1(a(n), ", "))
%Y Cf. A107086, A107089, A228711, A228712.
%K sign
%O 0,3
%A _Paul D. Hanna_, Mar 11 2013
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