[seqfan] can someone check this sequence for me.please?

[David Newman]

Here's a sequence which I'd like someone to check for errors before I
submit it.

Let a(n) be the number of partitions of n where the largest part, k, is
used once, the next smallest part has frequency <= 2, the next smallest
summand has frequency  <=3, etc.

For example: for n=6 the partitions counted are: 6 ,  5+1, 4+2, 4+1+1,
3+2+1. So, a(6)=5.

The first few values that I get are: 1,1,1,2,3,4,5,8,11,15,19