[seqfan] Re: n-multisets of integers in (-n..n} adding to n

[William Keith]

On Thu, Apr 12, 2012 at 9:03 AM, David Scambler <dscambler at bmm.com> wrote:

> Seqfans,
>
> Count all n-multisets of integers in {-n, ..., n} such that the members
> sum to n.
>
> a(n) = 1, 2, 7, 27, 121, 587, 2983, 15744, 85375, 473259, 2670383,
> 15293119, 88686530, 519864702,...
>
> Exclude zero as a member
>
> a(n) = 1, 1, 5, 17, 78, 375, 1919, 10144, 55189, 306632, 1734019, 9948977,
> 57790152, 339241199,...
>
> I shall submit with mma program if of interest.
>
> dave
>

David:

     You may be interested in a paper by George Andrews that talks about
"signed partitions," which are similar to this object.  There are many
related sequences which could be submitted.

Andrews: Euler's "De Partitio Numerorum." *Bulletin AMS* 44(4):561-573
(2007)

I published a brief followup, as his recently-graduated student, which is
available online at doi: 10.1007/s00026-011-0085-6 .

Cordially,
William Keith