Prove that the coefficient of x^p in the
expansion of (a_0 +a_1 x+a_2 x^2 +a_3 x^3 +...+a_k x^k )^n
is Σ((n!)/(n_0 !n_1 !n_2 !n_3 !...n_k !))a_0 ^n_0 a_1 ^n_1 a_2 ^n_2 a_3 ^n_3 ...a_k ^n_k
where n_0 , n_1 , n_2 , n_3 , ..., n_k are all non-
negative integers subject to the
conditions n_0 +n_1 +n_2 +n_3 +...+n_k =n
and n_1 +2n_2 +3n_3 +...+kn_k =p.
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