Dear R experts
I need to write a function that incorporates double summation, the problem
being that the upper limit of the second summation is the index of the first
summation, i.e:

sum_{j=0}^{x} sum_{i=0}^{j} choose(i+j, i)

where x variable or constant, doesn't matter.
The following code obviously doesn't work:

f=function(x) {j=0:x; i=0:j; sum( choose(i+j,i) )  }

Can you help?
Thanks in advance,

Orestis Chrysafis
School of Mathematics
University of Sheffield

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