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How to determine the probability given the PGF?

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#probability-theory #generating-functions
617
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PGF of total population of a branching process

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#stochastic-processes #generating-functions
145
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How to determine cumulative distribution function of a random variable?

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#probability-theory #probability-distributions #generating-functions
456
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Generating series for binary string not containing a substring

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#combinatorics #generating-functions
58
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$1-\sqrt{1-4p(1-p)s^2}$

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#probability #probability-theory #generating-functions
86
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Non linear recursive sequence bounds: $14\le R_{100} \le 18$.

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#sequences-and-series #inequality #recurrence-relations #generating-functions #recursion
63
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Couple questions on generating functions

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#generating-functions
1.9k
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A generating function for ordered Bell numbers

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#combinatorics #generating-functions
177
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A generating function $G(x)=-\frac{\frac{1}{x^5}(1+\frac{1}{x})(1-\frac{1}{x^2})}{((1-\frac{1}{x})(1-\frac{1}{x^3}))^2}$ related to partitions of $6n$

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#sequences-and-series #combinatorics #elementary-number-theory #generating-functions #integer-partitions
429
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What is the fastest way to calculate the $n$th coefficient of a generating function Modulo a prime $p$

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#combinatorics #number-theory #generating-functions
1.1k
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How many bit strings of length $n$ contain exactly $k$ blocks of "$10$"?

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#combinatorics #generating-functions
509
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Enumerative interpretation of generalized $q$-hockey stick identity

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#combinatorics #binomial-coefficients #finite-fields #generating-functions #q-analogs
173
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generating function of summation equation

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#combinatorics #generating-functions
369
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Check solution of recurrence relation $a_0 = 3$, $a_1 = 7$, $a_n = 3a_{n-1} - 2a_{n-2}$ for $n \geq 2$

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#combinatorics #recurrence-relations #generating-functions
148
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Coefficient of $x^r$ in $\frac{1}{(1-ax)^n}$

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#combinatorics #generating-functions

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