A "doublely-recursive" sequence

[Leroy Quet]

I just posted the below to sci.math.
(This particular sequence is, in my opinion, far from the most 
interesting/fundamental sequence I have yet to post to the EIS. But my 
computer's copy of Mathematica is not working properly after a crash; and 
I am too lazy even to suggest the other sequences on this email list. 
...but maybe someday..)

---- 

sci.math post:"a[m] = sum{j=0 to a[m-1](mod m)} a[j]"

If I did not make a mistake calculating the first few terms by hand,
here is a recursively-defined sequence which is not in the EIS yet.

a[0] = 1;

and for m >= 1, 

a[m] = sum{j=0 to a[m-1](mod m)} a[j]

Ascii-art:
       a[m-1](mod m)
        ---
        \
a[m] =  /      a[k]
        ---
        k=0


And,  0 <= a[m-1](mod m) <= m-1.


The sequence begins (maybe):

1, 1, 2, 4, 1, 2, 4, 9, 2, 4, 9, 30, 15,...

What can be said about this sequence? Does it have a closed-form (ie
nonrecursive) representation?

Also, other sequences can be based on the same idea: a partial sum
somehow involving earlier terms, BOTH in the general term and in the
limit of the indexes used in the sum.

Thanks,
Leroy Quet