a[m+1]=product{k=1 to m}(a[k]+a[m+1-k])

[Leroy Quet]

Let a[1] =1,
let a[m+1] = product{k=1 to m} (a[k] + a[m+1-k]).

The sequence begins:
1,2,9,400,19456921,...

and is sequence A049299 of the EIS.


What is the limit, as m->infinity, of log(a[m+1])/log(a[m]) ?
It appears to be about 3.

(I wondered back in 1999 about this, but I will bring up the question 
again now with seq.fan.)
 
Thanks,
Leroy Quet