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E.g.f.: A(x) = 1 + x + 4*x^2/2! + 27*x^3/3! + 304*x^4/4! +...
log(A(x)) = x + 3*x^2/2! + 17*x^3/3! + 190*x^4/4! + 3889*x^5/5! +...
log(A(x)) = (D^1 e^x) + (D^2 e^x)^2/2 + (D^3 e^x)^3/3 +...
D^1 exp(x) = (1)*x*exp(x);
D^2 exp(x) = (1 + x)*x*exp(x);
D^3 exp(x) = (1 + 3*x + x^2)*x*exp(x);
D^4 exp(x) = (1 + 7*x + 6*x^2 + x^3)*x*exp(x);
D^5 exp(x) = (1 + 15*x + 25*x^2 + 10*x^3 + x^4)*x*exp(x); ...
D^n exp(x) = n-th iteration of operator D = x*d/dx on exp(x)
equals the g.f. of the n-th row of triangle A008277 (S2(n,k))
times x*exp(x), and so is related to the n-th Bell number.
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