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A171188 G.f. satisfies: AGM(1,A(x)) = 1 + 4*x. 1

%I

%S 1,8,8,-16,48,-160,528,-1600,3952,-4512,-31040,322496,-2021584,

%T 10452384,-47768512,196396032,-719709808,2244001312,-5014625888,

%U -511332480,96425281504,-773680460288,4504107424128,-22283547559808,97629901795824

%N G.f. satisfies: AGM(1,A(x)) = 1 + 4*x.

%e G.f.: A(x) = 1 + 8*x + 8*x^2 - 16*x^3 + 48*x^4 - 160*x^5 + 528*x^6 +...

%e A(x)^(1/2) = 1 + 4*x - 4*x^2 + 8*x^3 - 16*x^4 + 16*x^5 + 104*x^6 +...

%e (1+A(x))/2 = 1 + 4*x + 4*x^2 - 8*x^3 + 24*x^4 - 80*x^5 + 264*x^6 +...

%o (PARI) {a(n)=local(A=1+8*x+sum(m=2,n-1,a(m)*x^m)+x^2*O(x^n));if(n<2,polcoeff(A,n),-2*polcoeff(agm(1,A),n))}

%Y Cf. A171189.

%K sign

%O 0,2

%A _Paul D. Hanna_, Dec 11 2009

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Last modified February 28 09:24 EST 2021. Contains 341695 sequences. (Running on oeis4.)