[seqfan] Question about A000290

[Prof. Dr. Alois Heinz]

Seqfans, in A000290 (The squares: a(n) = n^2.)

http://www.research.att.com/~njas/sequences/A000290

I found this comment: "a(n) is also the number of all partitions
 of the sum 2^2+2^2+...2^2, (n-1)-times, into powers of 2."

which is only partly true.

For n=3, we have the sum 2^2+2^2=8, but there are 10 (not 3^2=9)
partitions of 8 into powers of 2:
 
1+1+1+1+1+1+1+1, 1+1+1+1+1+1+2, 1+1+1+1+2+2, 1+1+2+2+2, 2+2+2+2
1+1+1+1+4, 1+1+2+4, 2+2+4, 4+4, 8

Perhaps the following was meant:

"a(n+1) is also the number of partitions of 4n into the first 3 powers
of 2 (parts of size 1, 2, 4)."

As FORMULA:  a(n) = [x^(4*n)] x^4/((1-x)*(1-x^2)*(1-x^4)).

Do you agree?

Alois