Multiply/Add Consecutive Integers

[Leroy Quet]

I was wondering today about the sequence where a(n) is the number of ways 
to get to n by:


1 (+,*) 2 (+,*) 3 (+,*) ....(+,*) m = n,

where we have the first m positive integers, in order, each separated by 
+ or multiply-by.
Order of operation is followed, and there is no parentheses or 
concatenation.


For example, since


15 =
1 + 2 +3*4 =
1 + 2 + 3 + 4 + 5 =
1*2*3 + 4 + 5,

we have a(15)  = 3 (or at least 3).

I have, figured by hand (so maybe wrong),

a(k) ->
1, 1, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 0, 2, 3,... 

And this is not in the EIS.

Is there any closed form for this sequence?

(I assume the minimum n for a given m is n= m(m+1)/2 -1 {1*2, rest are 
+'s}, and the maximum n is n= m! +1,{1+2, the rest are *'s}.)
 
thanks,
Leroy Quet