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How can we write a programmable multinomial expansion? I mean the summation over all non-negative integer indices, is somewhat difficult to program in Mathematica, at least for me. Is there any suggestions, please?

I saw this formula at the Mathematica official website, but I didn't know how to interpret it:

[tex]\left(a_1+a_2+\cdots+a_m\right)^n=\sum_{n_1,n_2,\dots,n_m=0}\delta_{n;n_1+n_2+\cdots+n_m}\left(n;n_1,n_2,\ldots,n_m\right)\prod_{k=1}^ma_k^{n_k}[/tex]

what does it mean [tex]n_1,n_2,\ldots,n_m=0[/tex]? and what is the delta function [tex]\delta_{n;n_1+n_2+\cdots+n_m}\left(n;n_1,n_2,\ldots,n_m\right)[/tex]??

Thanks in advance

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# Programmable Multinomial Expansion

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