# [seqfan] Re: conjectured EGF and extension of A086365 and others

Joerg Arndt arndt at jjj.de
Fri Apr 16 10:34:33 CEST 2010

```[copy to author of the sequence]

I think the desciption "symmetric set partition"
(set partitions of {-n,..,-1,+1,..n} such that
for each set Xi in the partition the negated set -Xi
is also in the partition) is wrong.

EXAMPLE a(2)=4
because the relevant partitions of {-2,-1,1,2} are
{-2|-1|1|2}, (#1)
{-2,-1|1,2}, (#2)
{-2,1|-1,2}, (#3)
{-2,-1,1,2}. (#4)

Why is {-2|-1,1|2} missing?
Set partition Number (#4) indicates
that the negative set -Xi is not required
to be distinct from Xi.

@James: is the EGF below correct?

Once things are clarified I'll edit A086365
(e.g. move definition of 'symmetric' into
a comment).  Seq A086364 might also need editing.

cheers,  jj

* Joerg Arndt <arndt at jjj.de> [Apr 16. 2010 09:01]:
>
> default(seriesprecision,66) \\ this many terms
>
> t(i)=Vec(serlaplace(exp(-x+sum(j=1,i,((exp(j*x)-1)/j)))))
> A000296:
>  t(1)
> [1, 0, 1, 1, 4, 11, 41, 162, 715, ...
>
> A086365:
> t(2)
> [1, 1, 4, 15, 75, 428, 2781, 20093, ...
> (could add more terms to OEIS entry)
>
> t(3)
> [1, 2, 10, 58, 416, 3450, 32356, 336838 ... not in OEIS (add?)
> [...]

```