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%I #2 Mar 30 2012 18:37:22
%S 1,1,-2,12,-120,1684,-31120,730167,-21231238,750298888,-31687276404,
%T 1575667784824,-91052587870552,6045175643449008,-456560323906523200,
%U 38886167319641201692,-3706800668529432678016,392824268201002386964776
%N G.f. A(x) satisfies: [x^n] A_{n-1}(x) = [x^n] A_{n-2}(x) for n>2 where A_{n+1}(x) = A_{n}(A(x)) denotes iteration with A_0(x)=x.
%e G.f.: A(x) = x + x^2 - 4*x^3 + 39*x^4 - 580*x^5 + 11480*x^6 +...
%e Coefficients in the initial iterations of A(x) begin:
%e [1, 1,(-2),. 12,. -120,. 1684,. -31120,.. 730167,. -21231238,...];
%e [1, 2,(-2), (15), -166,. 2482,. -48156,. 1173206,. -35125518,...];
%e [1, 3,. 0,. (15),(-180), 2832,. -57240,. 1438754,. -44147898,...];
%e [1, 4,. 4,.. 18, (-180),(2950), -61708,. 1591568,. -49868346,...];
%e [1, 5, 10,.. 30,. -160, (2950),(-63432), 1671151,. -53317312,...];
%e [1, 6, 18,.. 57,.. -90,. 2964, (-63432),(1702414), -55189776,...];
%e [1, 7, 28,. 105,... 84,. 3262,. -61768, (1702414),(-55964444),...];
%e [1, 8, 40,. 180,.. 440,. 4372,. -56712,. 1688208, (-55964444),...]; ...
%e where the above coefficients in parenthesis illustrate the property
%e that the coefficients of x^n in A_{n-1}(x) and in A_{n-2}(x) are equal.
%o (PARI) {a(n)=local(F=x+x^2+sum(m=3,n-1,a(m)*x^m)+x*O(x^n),G=x,H); for(i=1,n-2,G=subst(G,x,F));H=subst(G,x,F); if(n<1,0,if(n<3,1,polcoeff(G-H,n)))}
%Y Cf. A177775, A177776.
%K sign
%O 1,3
%A _Paul D. Hanna_, May 13 2010
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