# [seqfan] need help calculating

David Newman davidsnewman at gmail.com
Sun May 19 18:49:56 CEST 2013

```sequence A05342 asks for the number of partitions into "distinct parts"
where each of the parts is itself a finite subset of the integers and the
sum of the partition is the sum of all the integers in the set.

What is the number of partitions of n if the sets are closed under union?

For example:  A05342 gives four partition of 4.  Namely ( (4) ), ( (3,1)
) , ( (3), (1) ), ( (2,1), (1) )

The third of these, ( (3), (1) ), would not be counted if we require that
the sets be closed under union, since the union of the two singletons (3)
and (1) is not an element of the partition.

The idea of this sequence is from a famous conjecture by Frankl.

The values that I've gotten so far are, for n=1,2,...,11 :
1,1,2,3,5,6,9,11, 15, 21 28

I can't trust my hand computations and will be away from my copy of
Mathematica until August.

Anyone out there willing to verify and extend these numbers?
```