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How to show that inequality of a combinatoric series holds true

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#combinatorics #binomial-theorem #multinomial-theorem
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Expectation for Trinomial distribution

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#expectation #bivariate-distributions #multinomial-theorem
1.2k
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What is the coefficient of $x^5$ in the expression $(2 + x - x^2)^5$

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#multinomial-coefficients #multinomial-theorem
2.7k
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Find the the coefficient of $\,x^r\,$ in $\,(1+x+x^2)^n$

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#sequences-and-series #taylor-expansion #binomial-coefficients #multinomial-theorem
509
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Proving the Multinomial Theorem--Collapsing Double Sum (Multiple Summation Step)

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#discrete-mathematics #summation #multinomial-theorem
562
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Negative multinomial theorem?

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#binomial-theorem #multinomial-theorem
678
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Number of positive integral solutions in the given inequality

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#multinomial-coefficients #multinomial-theorem
77
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Coefficient of x in a geometric sum raised to the power of n

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#multinomial-coefficients #multinomial-theorem
125
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closed-form expression for expected value, $E\left\{X_1\cdots X_k\right\}$ for multinomial distribution

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#combinatorics #expectation #determinant #multinomial-coefficients #multinomial-theorem
244
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Simplified $\sum_{n=a_1k_1+a_2k_2+\cdots+a_mk_m}\frac{(a_1+a_1+\cdots+a_m)!}{a_1!\cdot a_2!\cdots a_m!}\prod_{i=1}^m \left(f(k_i)\right)^{a_i}$

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#combinatorics #summation #binomial-coefficients #integer-partitions #multinomial-theorem
230
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Prove that the general norm equation satisfies the triangle inequality for n-dimensions

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#real-analysis #functional-analysis #normed-spaces #multinomial-theorem
56
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Need help finding a sum

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#summation #multinomial-theorem
720
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Expansion of summation of power series raised to a power

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#sequences-and-series #summation #power-series #multinomial-coefficients #multinomial-theorem
186
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Find Coefficient of Trinomial Where Term has a Coefficient

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#combinatorics #multinomial-coefficients #multinomial-theorem
99
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Simplifying $ \sum_{1\cdot m_1 + 2\cdot m_2 + \cdots + n \cdot m_n = n} \frac{1}{m_1 ! m_2 ! \cdots m_n !} t^{m_1 + \cdots + m_n} $

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#combinatorics #generating-functions #multinomial-coefficients #multinomial-theorem

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