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EXAMPLE
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List the coefficients of powers of e.g.f. A(x) = Sum_{n>=0} a(n)*x^n/n!:
A(x)^0: [1,__0,0,0,0,0,0,0,0,...],
A(x)^1: [1,1,__3,-3,-57,369,3861,-76617,-413775,...],
A(x)^2: [1,2,8,__12,-84,-12,7200,-40716,-1301328,...],
A(x)^3: [1,3,15,51,__27,-513,4077,33237,-1211895,...],
A(x)^4: [1,4,24,120,408,__216,-3168,45576,-202176,...],
A(x)^5: [1,5,35,225,1215,4365,__1485,-27765,440865,...],...
then for each row n, Sum_{k=0..n} (A(x)^n)_k/k! = [exp(n)]:
[exp(0)] = 1 = 1
[exp(1)] = 1+1 = 2
[exp(2)] = 1+2+8/2! = 7
[exp(3)] = 1+3+15/2!+51/3! = 20
[exp(4)] = 1+4+24/2!+120/3!+408/4! = 54
[exp(5)] = 1+5+35/2!+225/3!+1215/4!+4365/5! = 148
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PROGRAM
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(PARI) {a(n)=local(A, C, F, G); if(n==0, A=1, F=sum(k=0, n-1, a(k)*x^k/k!); C=floor(exp(n))-sum(k=0, n-1, polcoeff(F^n+x*O(x^k), k, x)); G=sum(k=0, n-1, polcoeff(F^n+x*O(x^k), k, x)*x^k); A=n!*polcoeff((G+C*x^n)^(1/n)+x*O(x^n), n, x)); A}
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