A multinomial series is generalization of the binomial series discovered by Johann Bernoulli and Leibniz. The multinomial series arises in a generalization of the binomial distribution called the multinomial distribution. It is given by (a_1 + a_2 + ... + a_k)^n = sum_(n_1, n_2, ..., n_k>=0 n_1 + n_2 + ... + n_k = n) (n!)/(n_1 !n_2 !...n_k !) a_1^(n_1) a_2^(n_2) ...(a_k)^(n_k), where n congruent n_1 + n_2 + ... + n_k. For example, (a_1 + a_2 + a_3)^3 = a_1^3 + 3a_1^2 a_2 + 3a_1 a_2^2 + a_2^3 + 3a_1^2 a_3 + 6a_1 a_2 a_3 + 3a_2^2 a_3 + 3a_1 a_3^2 + 3a_2 a_3^2 + a_3^3.
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