I have an array of numbers lets call it $p$ , where $p[r]={k+r-1\choose k-1}$
I want to find the sum of all the elements of $p$ taken $n$ at a time .
$0\le r\le k$
For instance, for $k=3$ ,$n=2$ , i need
$$p[0]^2+p[1]^2+p[2]^2+p[3]^2+p[0]\cdot p[1]+p[0]\cdot p[2]+p[0]\cdot p[3]+p[1]\cdot p[2]+p[1]\cdot p[3]+\\+p[2]\cdot p[3]=\sum_{i\le j}p[i]\cdot p[j]=\sum_{i\le j}{k+i-1\choose k-1}{k+j-1\choose k-1}$$ which is $273$
Is there any way , i can solve this for any value of $k$ or $n$ without solving big equations like above
In other words , how to solve this summation?
$$\sum_{0\le x_1\le x_2...\le x_n \le n}^{}\binom{k+x_1-1}{x_1}\binom{k+x_2-1}{x_2}...\binom{k+x_n-1}{x_n}$$