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Calculating $\sum\limits_{i = r}^{n}{ {{i}\choose{r}} x^i}$

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#combinatorics #generating-functions
224
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How to find asymptotic expansion of $\frac{1}{\cos(z)}$

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#combinatorics #asymptotics #exponential-function #generating-functions #singularity
86
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Showing $\prod_{n\geq 1} (1+q^{2n}) = 1 + \sum_{n\geq 1} \frac{q^{n(n+1)}}{\prod_{i=1}^n (1-q^{2i})}$

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#number-theory #summation #generating-functions #infinite-product #integer-partitions
161
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Asymptotics in generating functions, am I doing right?

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#combinatorics #asymptotics #exponential-function #generating-functions #analyticity
338
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Formal power series and the quadratic formula

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#combinatorics #generating-functions #catalan-numbers #formal-power-series
504
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Determine the generating function for the sequence $a_n = 2^n n^2$

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#abstract-algebra #sequences-and-series #discrete-mathematics #binomial-coefficients #generating-functions
342
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Analyzing the Coefficient of a generating function and its asymptotic

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#combinatorics #asymptotics #generating-functions
71
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Usage of generating functions in the given enumeration problem

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#combinatorics #generating-functions
44
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Given $16$ pens to be distributed between $4$ people ,then find the number of distributions with the given assumptions.

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#combinatorics #generating-functions
171
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Stuck on a step for finding the closed formula for catalan numbers from generating function!

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#proof-explanation #binomial-coefficients #generating-functions #catalan-numbers
61
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How to solve $a+b+c=6; 2\le a\le 5, 2\le b\le 4, 1\le c\le 2$ with Generating Functions?

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#generating-functions
128
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Find generating function for linear recurrence

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#generating-functions #recursion
343
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Moving from a rational generating function to recurrence relation

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#discrete-mathematics #recurrence-relations #generating-functions
246
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Interesting question regarding generating function on words

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#combinatorics #asymptotics #generating-functions #combinatorics-on-words
260
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Deriving Generating function for centered trinomial coefficients

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#sequences-and-series #limits #generating-functions #multinomial-coefficients

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