A193379 - OEIS

%I #7 Jun 13 2012 14:26:40

%S 1,1,4,17,20,212,464,4361,17812,60532,123088,4117252,29724752,

%T 84585040,430795584,8219554697,47479991380,214977407060,898098431312,

%U 16268050731620,98128441675472,417822285118032,1654860158000960,35730391312348996,243329575991962320

%N Norm of coefficients in g.f. C(x) that satisfies: C(x) = 1 + x*C(I*x)^2.

%H Paul D. Hanna, <a href="/A193379/b193379.txt">Table of n, a(n) for n = 0..200</a>

%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);norm(polcoeff(A,n))}

%Y Cf. A193377 (real), A193378 (imag).

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jul 24 2011