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A158212 A quadrisection of A158122: a(n) = A158122(4n).

%I A158212 #5 Mar 30 2012 18:37:16
%S A158212 1,2,-16,200,-3006,49956,-884352,16349648,-311986480,6098614912,
%T A158212 -121497078016,2457844837376,-50353474318552,1042571366405520,
%U A158212 -21781950163497216,458626034728146240,-9721961867347898174
%N A158212 A quadrisection of A158122: a(n) = A158122(4n).
%C A158212 See A060691 for the expansion of AGM(1,1-8x), where AGM denotes the arithmetic-geometric mean.
%H A158212 Paul D. Hanna, <a href="/A158212/b158212.txt">Table of n, a(n) for n=0..100</a>
%F A158212 G.f.: A(x) = 2/B(x) where B(x) is the g.f. of A158213;
%F A158212 let F(x) = A(x^4) + 2*x/A(x^4) be the g.f. of A158122
%F A158212 then F(x) satisfies: F(x)^2 = 1/AGM(1, 1 - 8*x/F(x)^2 ).
%e A158212 G.f.: A(x) = 1 + 2*x - 16*x^2 + 200*x^3 - 3006*x^4 + 49956*x^5 +...
%e A158212 2/A(x) = 2 - 4*x + 40*x^2 - 544*x^3 + 8540*x^4 - 145720*x^5 +...
%e A158212 F(x) = 1 + 2*x + 2*x^4 - 4*x^5 - 16*x^8 + 40*x^9 + 200*x^12 - 544*x^13 +...
%o A158212 (PARI) {a(n)=polcoeff(sqrt(x/serreverse(x/agm(1,1-8*x +O(x^(4*n+1))))),4*n)}
%Y A158212 Cf. A158122, A158213, A158100, A060691.
%K A158212 sign
%O A158212 0,2
%A A158212 _Paul D. Hanna_, Mar 14 2009