The successive iterations of g.f. A(x) begin:
A(x) = (1)x + x^2 - 2x^3 + 8x^4 - 40x^5 + 210x^6 - 1032x^7 + 4074x^8+..
A(A(x)) = x + (2)x^2 - 2x^3 + 7x^4 - 30x^5 + 118x^6 -268x^7 -1430x^8+..
A(A(A(x))) = x + 3x^2 + (0)x^3 + 3x^4 -12x^5 +18x^6 +240x^7 -3119x^8+..
A(A(A(A(x)))) = x + 4x^2 + 4x^3 + (2)x^4 - 4x^5 - 18x^6 + 276x^7+...
A(A(A(A(A(x))))) = x + 5x^2 + 10x^3 + 10x^4 +(0)x^5 -20*x^6 +128*x^7+..
A(A(A(A(A(A(x)))))) = x + 6x^2 + 18x^3 +33x^4 +30x^5 +(0)x^6 -24x^7+..
Coefficients [x^n] of n-th iteration of A(x) forms
A119818:
[1,2,0,2,0,0,0,0,0,0,0,10,0,0,7,12,0,6,0,9,2,11,0,8,10,13,18,18,...].
