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Can this be proved using Combinatorics or generating functions?

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#combinatorics #summation #binomial-coefficients #generating-functions #combinatorial-proofs
137
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Generating Functions VS Z-Transforms as Solutions to Recurrence Relations

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#discrete-mathematics #recurrence-relations #generating-functions #signal-processing #z-transform
69
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How do u prove $\sum_{k=0}^n\frac{1}{2^{k}}\binom{n+k}{n} = 2^{n}$?

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#combinatorics #summation #generating-functions
83
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Coefficient Extraction of Products of Generating Functions

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#sequences-and-series #discrete-mathematics #power-series #generating-functions
279
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A company hires $11$ new employees, and they will be assigned to four different departments, A, B, C, D

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#combinatorics #generating-functions
91
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Where do the powers go?

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#reference-request #power-series #generating-functions #formal-power-series
41
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Deriving a generating function from a pdf

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#calculus #probability #integration #generating-functions
45
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Generating function and functional equation

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#combinatorics #probability-theory #generating-functions
52
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Probability generating functions understanding

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#probability #stochastic-processes #generating-functions
251
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Prove that $\sum_i {n\choose i}{2n\choose n-i}={3n\choose n}$.

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#combinatorics #generating-functions
123
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Galton Watson and generating function

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#probability #probability-theory #generating-functions
225
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Derive the Probability Generating Function for a Series of Bernoulli Trials

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#probability #probability-distributions #generating-functions
102
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generating function for k-combinations

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#combinatorics #combinations #generating-functions
50
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Infinite product formula for $\sum_{n \geq 0} p_e(n)\cdot x^n$

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#combinatorics #generating-functions #infinite-product #integer-partitions
109
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number of positive integer solutions of $x+y+z+w=24$

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#combinatorics #permutations #binomial-coefficients #generating-functions

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