I'd like to know whether the following is known (I bet it is, and in a more general context): cf. https://oeis.org/A187761 and https://oeis.org/A179455 Let C(n,x) be the e.g.f of the monotonic-labeled forests on n vertices with rooted trees of height less than n. (A labeled rooted tree is monotonic-labeled if the label of any parent vertex is (strictly) smaller than the label of any offspring vertex.) I conjecture that the C(n,x) are as follows. Let C(0,x) = 1 and for n>=1, C(n, x) = exp(integral(C(n-1,x)) ) For n=1 (C(1,x)=exp(x), constant sequence of ones) and n=2 (C(2,x)=exp(exp(x)-1), Bell numbers) this is obviously true. (note that integration of an e.g.f. essentially shifts it to smaller powers and drops the constant term; for the corresponding sequences: it just drops the first term). So clueless, jj