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Proof of Chu–Vandermonde identity

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#combinatorics #probability-theory #binomial-coefficients #binomial-theorem
95
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Series representation for $(1+x)^{n-m}(1-x)^{m}$

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#combinatorics #binomial-coefficients #closed-form
51
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Prove that $(1 + z)^x \cdot (1+z)^y = (1+z)^{(x+y)}$ for formal power series

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#binomial-coefficients #formal-power-series
71
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Coefficient of $x^4y^3z^3$ in the expansion of $(5x+y-4z)^{10}$

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#discrete-mathematics #binomial-coefficients #multinomial-coefficients
971
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Binomial coefficients modulo a prime

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#modular-arithmetic #binomial-coefficients #finite-fields
128
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Every natural number can be expressed uniquely as the sum of $k$ binomial coefficients

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#combinatorics #discrete-mathematics #binomial-coefficients
84
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$\sum_{k=0}^n \binom{n}{k}\frac{(-1)^k}{k!}(k+m)!=0$.

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#combinatorics #binomial-coefficients
67
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Concrete Mathematics, The conditions of formula(5.12)

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#binomial-coefficients #absolute-convergence
189
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Infinite sum with binomial coeffcient - Hypergeometric function ${}_2F_1$ and gauss theorem

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#sequences-and-series #binomial-coefficients #hypergeometric-function
48
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How can I prove that this sequence is correct?

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#sequences-and-series #binomial-coefficients
351
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How to estimate (approximate) $\sum _{k=1}^{n}{\log(k)\binom {n}{k}}$?

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#probability #combinatorics #probability-theory #binomial-coefficients
279
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Infinite sum - generalising Catalan generating function

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#sequences-and-series #binomial-coefficients #hypergeometric-function #catalan-numbers
61
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Does Pascal’s Triangle Form Hypercubes?

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#geometry #binomial-coefficients
64
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Sum of products of binomial coefficients

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#combinatorics #binomial-coefficients #generating-functions
144
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sum of adjacent number in a triangle Ask

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#binomial-coefficients #arithmetic-progressions

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