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Generating function expansion

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#combinatorics #generating-functions
814
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Generating function for the sequence $(a_k) = (1,-1,2,-2,3,-3,4,-4,...).$

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#sequences-and-series #combinatorics #generating-functions
104
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Find the PGF of the discrete random variable X with probability mass function

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#probability #probability-distributions #generating-functions #expected-value #variance
655
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Using generating function to find total no. of ways to collect 15 dollars given the particular restrictions

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#combinatorics #generating-functions
240
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Finding the generating function of $\sum_{k=1}^n k^2$

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#combinatorics #summation #generating-functions
40
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generating function of Fibonacci sequence: a wrong answer

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#generating-functions
793
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In how many ways $A_n$ can we cover a $2 \times n$ rectangle with $1 \times 2$ and $2 \times 2$ polyominoes?

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#recurrence-relations #generating-functions #tiling #polyomino
75
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Proving a recursive relation of Probability Generating Functions

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#probability #probability-theory #stochastic-processes #generating-functions
59
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Recurrence relation problem with $a_{n-1}=2a_n+4^n$ for $n\geqslant 0$, and $a_1=3$.

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#discrete-mathematics #recurrence-relations #power-series #generating-functions
41
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One property of a power series

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#polynomials #operator-theory #power-series #partial-derivative #generating-functions
80
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Using generating functions to translate a word problem into a recurrence relation?

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#combinatorics #generating-functions
33
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$r$-Permutations of $n$ things of $k_1,...,k_j$ kinds.

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#combinatorics #permutations #generating-functions
105
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Using Probability Generating Function to find probability

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#probability #statistics #probability-distributions #generating-functions
333
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Closed form of recurrence relation $a_k=(n+k)a_{k-1}-ka_{k-2}$

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#ordinary-differential-equations #recurrence-relations #generating-functions #closed-form
409
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Show that the Catalan numbers count the following

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#combinatorics #generating-functions #catalan-numbers

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