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Ordinary generating function and 1/(1 - x)

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Text Generating Functions: Do they exist?

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Number of partitions of integer into parts repeated <= 2 times

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#number-theory #generating-functions #integer-partitions
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How do you find generating function?

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#combinatorics #generating-functions
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finding probability generating function and the sum of two independent random variables

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#probability #random-variables #generating-functions
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Solving this recursive function $f(x)=f(x-k)+f(x/k)$.

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#sequences-and-series #algebra-precalculus #recurrence-relations #generating-functions
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Number of nodes with even offspring

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#generating-functions #trees
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Combinatorics - Find the coefficient of $x^{12}$ in...

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#combinatorics #binomial-coefficients #generating-functions
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Prove that $P_{S_N}(t) = P_N(P_X(t))$ for $S_N = X_1 + \cdots + X_N$.

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#probability #generating-functions
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We have n cards. We want to split them into an even number of non-empty subsets, form a line within each subset, then arrange the subsets in a line.

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#combinatorics #recurrence-relations #generating-functions
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finding an explicit formula for $a_n$ if$ a_0=1, a_1=4$, and $a_{n+2}=8a_{n+1} -16a_n$.

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#combinatorics #recurrence-relations #generating-functions
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Find closed form solution using generation function for the binomial coefficients

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#binomial-coefficients #generating-functions
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Ordinary generating function for $\binom{3n}{n}$

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#calculus #sequences-and-series #binomial-coefficients #generating-functions
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Using the generating function to find an identity relating Bessel functions

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#special-functions #generating-functions
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Multiplicative Inverse for Generating Function

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#combinatorics #power-series #generating-functions

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