a binomial sum.

[Robert G. Wilson v]

pin wrote:
> Hello seqfans!
> 
> I was about to submit the following signed sequence (offset 0),
> 
> 1, -1, 7, -21, 81, -295, 1107, -4165, 15793, -60171, 230253, -884235, 3406105, -13154947, 50922987, -197519941, 767502945, -2987013067, 11641557717, -45429853651, 177490745985, ...,
> 
> but thought that I post here first requesting if someone is able to find a closed form of it.  Here is the sum that generates the sequence in Maple code.
> 
> a:=n->sum(sum(binomial(j-n-1,m),m=0..n),j=0..n);

In Mathematica it is: Sum[Binomial[j - n - 1, m], {m, 0, n}, {j, 0, n}]

Bob.

> 
> Any ideas?
> 
> -Francois.
> 
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