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how to define this polynome?

$ h_i(x_1,\ldots,x_n) = \sum_{j_1+\cdots+j_n=i} \;\prod_{k=1}^n x_k^{j_k}$

I think I need a Partitions(i) to do it but I need some $j_k$ to be zero, then I tried PartitionTuples(level=n,size=i), and it still doesn't work.

how to define this polynome?

$ h_i(x_1,\ldots,x_n) = \sum_{j_1+\cdots+j_n=i} \;\prod_{k=1}^n x_k^{j_k}$

I think I need a Partitions(i) to do it but I need some $j_k$ to be zero, then I tried PartitionTuples(level=n,size=i), and it still doesn't work.