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How to use a generating function to work out an infinite sum

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#sequences-and-series #power-series #generating-functions
79
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Proving that $\sum_{n=1}^{\infty}S(n,n-2)x^n = \frac{x^3(1+2x)}{(1-x)^5}$

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#generating-functions #stirling-numbers
376
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The number of words of length $n$ from specific alphabet with rule of creating.

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#sequences-and-series #combinatorics #discrete-mathematics #recurrence-relations #generating-functions
53
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Not sure what I'm doing wrong with this recurrence problem

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#recurrence-relations #generating-functions
1.2k
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Why the moment-generating function, rather than the characteristic function?

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#probability-theory #statistics #generating-functions #moment-generating-functions
170
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How many combination of $3$ integers reach given number?

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#combinatorics #discrete-mathematics #permutations #generating-functions #integer-partitions
163
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Determine the EGF for a set of partitions of partitions.

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#combinatorics #generating-functions
650
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Partial fraction of a generating function

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#recurrence-relations #generating-functions #partial-fractions
2.1k
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Find the exponential generating function for the number of ways to distribute $r$ distinct objects into five different boxes

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#combinatorics #generating-functions #integer-partitions
339
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How many ways to choose $a<b<c<d<e$ from the set $\{1,2,3,\dotsc,100\}$ such that $100<a+b+c+d+e<145$?

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#combinatorics #generating-functions #integer-partitions
452
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Reindexing Exponential Generating Function

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#sequences-and-series #combinatorics #taylor-expansion #generating-functions #euler-maclaurin
1.4k
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Evaluate the following sums using generating functions

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#sequences-and-series #combinatorics #summation #generating-functions
436
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Can we characterize the probability generating function as a linear operator?

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#functional-analysis #probability-theory #soft-question #operator-theory #generating-functions
150
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Using generating functions to count

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#combinatorics #generating-functions
51
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prove the equation by generating functions

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#generating-functions

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