%I #4 Mar 30 2012 18:37:16
%S 2,-4,40,-544,8540,-145720,2625648,-49161024,947069352,-18650752400,
%T 373773754912,-7598155324032,156294309718944,-3247203559571136,
%U 68042170392274560,-1436308791802028544,30514944039812500572
%N A quadrisection of A158122: a(n) = A158122(4n+1).
%C See A060691 for the expansion of AGM(1,1-8x), where AGM denotes the arithmetic-geometric mean.
%F G.f.: A(x) = 2/B(x) where B(x) is the g.f. of A158212;
%F let F(x) = 2/A(x^4) + x*A(x^4) be the g.f. of A158122
%F then F(x) satisfies: F(x)^2 = 1/AGM(1, 1 - 8*x/F(x)^2 ).
%e G.f.: A(x) = 2 - 4*x + 40*x^2 - 544*x^3 + 8540*x^4 - 145720*x^5 +...
%e 2/A(x) = 1 + 2*x - 16*x^2 + 200*x^3 - 3006*x^4 + 49956*x^5 +...
%e F(x) = 1 + 2*x + 2*x^4 - 4*x^5 - 16*x^8 + 40*x^9 + 200*x^12 - 544*x^13 +...
%e where F(x) = 2/A(x^4) + x*A(x^4) is the g.f. of A158122.
%o (PARI) {a(n)=polcoeff(sqrt(x/serreverse(x/agm(1,1-8*x +O(x^(4*n+2))))),4*n+1)}
%Y Cf. A158122, A158212, A158100, A060691.
%K sign
%O 0,1
%A _Paul D. Hanna_, Mar 14 2009