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A277033 G.f. A(x) satisfies: A(x - A(-x)^2) = x + A(x)^2.

%I A277033 #8 Oct 09 2016 19:46:12
%S A277033 1,2,4,18,76,420,2248,14410,89676,642764,4487896,35282228,271094936,
%T A277033 2310824808,19309255952,177093587874,1596354765308,15664040851996,
%U A277033 151403517122328,1582290415072396,16319413287176584,180949924453071544,1983128441367699632,23249895784026465044,269763155110100504568,3333619355332522429656
%N A277033 G.f. A(x) satisfies: A(x - A(-x)^2) = x + A(x)^2.
%F A277033 G.f. A(x) satisfies: A(-A(-x)) = x.
%e A277033 G.f.: A(x) = x + 2*x^2 + 4*x^3 + 18*x^4 + 76*x^5 + 420*x^6 + 2248*x^7 + 14410*x^8 + 89676*x^9 + 642764*x^10 +...
%e A277033 such that A(x - A(-x)^2) = x + A(x)^2.
%e A277033 RELATED SERIES.
%e A277033 A(x)^2 = x^2 + 4*x^3 + 12*x^4 + 52*x^5 + 240*x^6 + 1288*x^7 + 7108*x^8 + 43908*x^9 + 275872*x^10 + 1904280*x^11 + 13301112*x^12 +...
%e A277033 sqrt((A(x) - x)/2) = x + x^2 + 4*x^3 + 15*x^4 + 82*x^5 + 420*x^6 + 2742*x^7 + 16767*x^8 + 123294*x^9 + 856042*x^10 + 6906790*x^11 + 53066832*x^12 +...
%e A277033 Series_Reversion( sqrt((A(x) - x)/2) ) = x - x^2 - 2*x^3 - 14*x^5 - 406*x^7 - 16514*x^9 - 872812*x^11 - 56605438*x^13 - 4346269882*x^15 - 386603411414*x^17 - 39262351744912*x^19 - 4504838187841052*x^21 -...
%o A277033 (PARI) {a(n) = my(A=x,R); for(i=1,n, R = subst(A,x,-x + x*O(x^n)); A = subst(x + A^2,x, serreverse(x - R^2))); polcoeff(A,n)}
%o A277033 for(n=1,30,print1(a(n),", "))
%Y A277033 Cf. A277034, A275765.
%K A277033 nonn
%O A277033 1,2
%A A277033 _Paul D. Hanna_, Oct 09 2016