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Finding exponential generating function

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#combinatorics #proof-writing #exponential-function #generating-functions
498
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How to solve the recurrence relation $a_{1}=2, a_{n}=\frac{a_{n-1}+2}{2 a_{n-1}+1}(n \geq 2)$ with generating functions?

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#sequences-and-series #recurrence-relations #systems-of-equations #generating-functions
56
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Find generating function for $\sum_{n\ge 0} \binom{m+n}{n}x^n$, $m \in\mathbb{Z}$

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#generating-functions
43
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Density of a set of numbers equal to limit at 1

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#real-analysis #generating-functions
167
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Karamata's proof of Hardy-Littlewood Tauberian theorem

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#real-analysis #generating-functions #tauberian-theory
83
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Find B(x) such that $A(x) = P(x) \cdot B(x) $

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#discrete-mathematics #polynomials #generating-functions #integer-partitions
198
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Prove $\sum_{k=0}^n \binom{2k}{k}\binom{2(n-k)}{n-k}=4^n$

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#generating-functions
447
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what is exponential generating function with n Choose k as coefficient

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#combinatorics #summation #exponential-function #generating-functions
45
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Finding formula for generating function coefficient

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#combinatorics #proof-writing #generating-functions
113
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Proof needed for the combinatorial identity $\sum_{a=0}^n\binom{n+a}{a}/{2^{n+a}}=1$

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#combinatorics #discrete-mathematics #binomial-coefficients #generating-functions #combinatorial-proofs
16
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A(x) is the generating function of the series $\{a_n\}^\infty $ ( n from 0), what generates,$f_n=(-1)^na_n$

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#generating-functions
43
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partition function - using each number once and using only odd numbers

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#generating-functions #integer-partitions
113
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Creating a generating function for the Stirling transform

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#combinatorics #generating-functions
55
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I'm having trouble finding the sequence generated by this function.

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#discrete-mathematics #generating-functions
58
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Asymptotics of the probability of passengers on wrong airplane seats

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#combinatorics #probability-distributions #asymptotics #generating-functions

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