[seqfan] Re: need help calculating

[David Newman]

I should have written A 050342 in my previous post.

On Sun, May 19, 2013 at 7:49 PM, David Newman <davidsnewman at gmail.com>wrote:

>  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?
>