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%I #7 Mar 30 2012 18:37:28
%S 1,1,0,-1,-4,-14,8,35,44,246,168,-1906,296,-5692,-19440,89539,-104836,
%T 110062,946856,-3306758,8516696,3998844,-36402256,82221230,-492938376,
%U -657397540,1092399120,553666748,22487269712,48307873544,-8248804576,-259354056349,-754908556068
%N Real part of g.f. C(x) that satisfies: C(x) = 1 + x*C(I*x)^2.
%e G.f.: C(x) = 1 + x + 2*I*x^2 + (-1 - 4*I)*x^3 + (-4 + 2*I)*x^4 + (-14 - 4*I)*x^5 + (8 - 20*I)*x^6 + (35 + 56*I)*x^7 + (44 - 126*I)*x^8 + (246 - 4*I)*x^9 + (168 + 308*I)*x^10 +...
%e where
%e C(x)^2 = 1 + 2*x + (1 + 4*I)*x^2 + (-2 - 4*I)*x^3 + (-14 - 4*I)*x^4 + (-20 - 8*I)*x^5 + (-35 - 56*I)*x^6 + (126 + 44*I)*x^7 + (246 - 4*I)*x^8 +...
%e The real part of the g.f. begins:
%e real(C(x)) = 1 + x - x^3 - 4*x^4 - 14*x^5 + 8*x^6 + 35*x^7 + 44*x^8 + 246*x^9 + 168*x^10 - 1906*x^11 + 296*x^12 +...
%e The imaginary part of the g.f. begins:
%e imag(C(x)) = 2*x^2 - 4*x^3 + 2*x^4 - 4*x^5 - 20*x^6 + 56*x^7 - 126*x^8 - 4*x^9 + 308*x^10 - 696*x^11 + 5444*x^12 +...
%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=1+x*subst(A,x,I*x +x*O(x^n))^2);real(polcoeff(A,n))}
%Y Cf. A193378 (imag), A193379 (norm).
%K sign
%O 0,5
%A _Paul D. Hanna_, Jul 24 2011
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