Neil, I had seen that formula but it was a long time ago and I had forgotten what it was for. It appears to be spot-on to answer my question. Thanks!! --Dan << Dan, You about Faa di Bruno's formula, right? Best regards Neil Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com << OK, I suppose Mathematica isn't going to answer my real question. Which is: Let u(x) be any infinitely differentiable function. Then if f(x) = exp(u(x)), its nth derivative f^(n)(x) (n >= 1) is a polynomial with positive integer coefficients in the derivatives u', u'', ..., u^(n), times exp(u(x)): f^(n)(x) = P_n(u', u'', ..., u^(n)) exp(u(x)) The polynomial P will be homogenous of (let's call it) "index" n if in each monomial, the factor u^(k) is assigned index k, and the indices of all factors are added. Using x_1,...,x_n as the variables in P_n, we'd have for instance P_3(x_1, x_2, x_3) = (x_1)^3 + 3 x_1 x_2 + x_3 Question: Is there a closed formula for P_n (without recursion) ? Do they have a specific name? What properties do they have? --Dan