E.g.f.'s and Tables

[franktaw at netscape.net]

For a table, there is more than one way to take the exponential generating function (e.g.f.).  One can take sum T(n,m) x^n/n! y^m, or sum T(n,m) x^n/n! y^m/m!.  (Or, of course, T(n,m) x^n y^m/m!.)
 
Most of the table sequences in the OEIS that have e.g.f.'s specified do not specify which e.g.f. is being evaluated.  The majority (based on a *very* cursory survey) appear to be of the first type.
 
I recommend that any e.g.f. for a table specify exactly what is being summed.  I have submitted changes for a few of these, mostly where both forms are interesting.  (Since Neil is on vacation, these won't show up until at least mid-month.)  Just for example, here is one of the changes I submitted:
 
%I A008279
%S A008279 1,1,1,1,2,2,1,3,6,6,1,4,12,24,24,1,5,20,60,120,120,1,6,30
%C A008279 Replace formula line "E.g.f.: exp(x)/(1-x*y). - Vladeta Jovovic 
(vladeta(AT)Eunet.yu), Aug 19 2002" with "E.g.f.: sum T(n,k) x^n/n! y^k = 
exp(x)/(1-x*y). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Aug 19 2002".
%F A008279 E.g.f. sum T(n,k) x^n/n! y^k/k! = e^{x+xy}.
%O A008279 0
%K A008279 ,easy,nice,nonn,tabl,
%A A008279 Frank Adams-Watters (FrankTAW(AT)Netscape.net), Feb 07 2006
 
Franklin T. Adams-Watters
16 W. Michigan Ave.
Palatine, IL 60067
847-776-7645
___________________________________________________
Try the New Netscape Mail Today!
Virtually Spam-Free | More Storage | Import Your Contact List
http://mail.netscape.com
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://list.seqfan.eu/pipermail/seqfan/attachments/20060207/cce6a127/attachment.htm>