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EXAMPLE
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G.f.: A(x) = x + x^2 - 2*x^3 + 6*x^4 - 24*x^5 - 820*x^6 + 27144*x^7 +...
Coefficients in the prime iterations of A(x) begin:
[1, 2, -2, 3, -10, -1818, 47740, -2337494, 105376812, ...];
[1, 3, 0, -3, 0, -2772, 60624, -3189473, 140910696, ...];
[1, 5, 10, 0, -40, -4650, 64048, -4546444, 185930620, ...];
[1, 7, 28, 63, 0, -6958, 36288, -5825281, 201609418, ...];
[1, 11, 88, 561, 2816, 0, -88880, -10110089, 134676036, ...];
[1, 13, 130, 1092, 7800, 34658, 0, -13180700, 29207048, ...];
[1, 17, 238, 2958, 33320, 327012, 2674984, 0, -240789190, ...];
[1, 19, 304, 4389, 58368, 703988, 7570512, 51417135, 0, ...];
[1, 23, 460, 8487, 147200, 2401338, 36774976, 501489263, 5774993410, 0, ...]; ...
where the coefficient of x^n in the prime(n-1) iteration of A(x) equals zero for n>2.
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PROG
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(PARI) {ITERATION(n, F)=local(G=x); for(i=1, n, G=subst(G, x, F)); G}
{a(n)=local(A=[1, 1]); for(i=1, n, A=concat(A, 0); A[#A]=-Vec(ITERATION(prime(#A-1), x*Ser(A)))[#A]/prime(#A-1)); A[n]}
for(n=1, 30, print1(a(n), ", "))
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