[seqfan] A sort of composition

[David Newman]

Count the number of compositions of n arranged in an array for which each
row length is less than or equal to the length of the row above it.
(Similar to a plane partition,but with no restriction that the summands be
decreasing along rows and columns.)

For example: for 3 there are 8 such compositions
3

2,1

1,2

2
1

1
2

1,1,1

1,1
1

1
1
1

The first few values that I get are 1,3,8,21,54,137

This matches four sequences in the OEIS, but it doesn't match any of the
definitions, as far as I can see .  Can someone out there tell me if it's
the same as one of the matches?