On 15/01/2013 18:17, Joerg Arndt wrote:
I cited (and (very slightly) rephrased), please peek at https://oeis.org/draft/A187761 and give your OK (else just edit):
------------------------ Gareth McCaughan, on the math-fun mailing list (Jan 14 2013), writes "If F is the e.g.f. for Things Of Size n, then exp(F) is the e.g.f. for Multisets Of Things Whose Sizes Add Up To n. (The factorials turn into multinomial coefficients.) Which means the conjecture is right. (The integral turns that into "multisets of things whose sizes plus 1 add up to n"; a tree is a forest together with a new node on top.) " ------------------------
Looks OK to me. I did a quick search and found this, which states and explains a nice general principle of which the above is a very special case. http://math.berkeley.edu/~mhaiman/math172.../exponential.pdf In particular, look at the section called "The function composition principle". (To be explicit: it generalizes what I said about applying exp to egfs; it doesn't generalize your discovery about labelled forests.) -- g