[seqfan] Highest exponent of 2 dividing A155200(n)

[Paul D Hanna]

Seqfans, 
       Regarding sequence A155200: 
http://www.research.att.com/~njas/sequences/A155200
G.f.: exp(Sum_{n>=1} 2^(n^2)*x^n/n) = 1 + 2*x + 10*x^2 + 188*x^3 + 16774*x^4 +...+ A155200(n)*x^n +... 
 
I propose the following 
CONJECTURE: 
Highest exponent of 2 dividing A155200(n) = A000120(n) = number of 1's in binary expansion of n, so that A155200(n)/2^A000120(n) is odd for n>=0. 
  
I have verified that this conjecture holds for n=0..1024. 
But I do not know why it should be true. 
 
A related question: 
is there an analogous formula for the highest exponent of 3 dividing A155203(n): 
http://www.research.att.com/~njas/sequences/A155203 
  
Wonder if anyone has an insight into these topics.  
     Paul