plane partitions

[Christian G. Bower]

I did some more playing with planar partitions.
Here is a triangle where n,k is the number of planar partitions with
exactly k rows.

1 
2 1 
3 2 1 
5 5 2 1 
7 9 5 2 1 
11 18 11 5 2 1 
15 30 22 11 5 2 1 
22 53 42 24 11 5 2 1 
30 85 78 46 24 11 5 2 1 
42 139 138 90 48 24 11 5 2 1 

(submitted as A091355)

I tried the Inverse Euler of it and got

1 
2 0 
3 0 0 
5 -1 0 0 
7 -2 0 0 0 
11 -5 0 0 0 0 
15 -10 2 0 0 0 0 
22 -20 6 0 0 0 0 0 
30 -35 16 -2 0 0 0 0 0 
42 -63 38 -7 0 0 0 0 0 0 
(not submitted)
which tells me I probably will not find a nice g.f. for it.
However, I noticed that the columns converge to:
1 2 5 11 24 48 96 182 342 624 1124 1983 3462 5947 ...
which is not in the EIS (submitted as A091360)
Superseeker was kind enough to tell me this is the partial sums
of A000219.

Christian