for (1,1) there will be 1 tree
for (2,2,1,1) there will be 2 trees
for (3,3,2,2,1,1) there will be 6 trees
for (4,4,3,3,2,2,1,1) there will be (4,4,3,3,2,2,1,1)
(4,4,3,2,3,2,1,1),(4,4,3,3,1,-,-,-),(4,4,3,1,3,-,-,-),(4,4,3,2,1,-,-,-),(4,4,3,1,2,-,-,-),(4,4,3,2,2,-,-,-)
Now also in 2nd highest level there are also 3 combinations
(4,3,4,-,-,-,-,-)
(4,4,2,-,-,-,-,-)
So, I think it will be more than 44