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A223142 G.f. satisfies: A(x)^2 = A(x^2)^2 + 4*x.

%I A223142 #5 Mar 15 2013 11:57:43
%S A223142 1,2,0,0,2,-4,8,-16,32,-56,88,-112,64,240,-1264,4064,-10814,25500,
%T A223142 -54200,102832,-166020,190808,22304,-1058880,4412424,-13496544,
%U A223142 35306480,-82326496,172081840,-315115328,464910368,-363016000,-871587808,5713552456,-20289991016
%N A223142 G.f. satisfies: A(x)^2 = A(x^2)^2 + 4*x.
%H A223142 Paul D. Hanna, <a href="/A223142/b223142.txt">Table of n, a(n) for n = 0..500</a>
%F A223142 G.f.: A(x) = sqrt( 1 + Sum_{n>=0} 4*x^(2^n) ).
%e A223142 G.f.: A(x) = 1 + 2*x + 2*x^4 - 4*x^5 + 8*x^6 - 16*x^7 + 32*x^8 - 56*x^9 +...
%e A223142 where
%e A223142 A(x)^2 = 1 + 4*x + 4*x^2 + 4*x^4 + 4*x^8 + 4*x^16 + 4*x^32 +...+ 4*x^(2^n) +...
%o A223142 (PARI) {a(n)=local(A=1+x); for(i=1,#binary(n), A=(subst(A, x, x^2)^2+4*x+x*O(x^n))^(1/2)); polcoeff(A, n, x)}
%o A223142 for(n=0,40,print1(a(n),", "))
%Y A223142 Cf. A223143, A107086, A223026.
%K A223142 sign
%O A223142 0,2
%A A223142 _Paul D. Hanna_, Mar 15 2013