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Interesting multiplicative Ramanujan-like q-expansions

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#generating-functions #infinite-product #modular-forms #multiplicative-function #ramanujan-summation
104
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Find the number of ways to fill $4$ different boxes with $14$ balls if the last box must not have more balls than the sum of the first three boxes

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#combinatorics #generating-functions
192
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Number of Paths on Complete 2-Digraph with Loops

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#combinatorics #graph-theory #combinations #generating-functions
77
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Combinatorial sum and generating functions

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#combinatorics #discrete-mathematics #generating-functions
192
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Stanley Enumerative Combinatorics 1.4

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#combinatorics #generating-functions
9.8k
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Proving the generating function of $n^2$

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#discrete-mathematics #generating-functions
708
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Generating function for number of partitions with only distinct even parts

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#discrete-mathematics #generating-functions #integer-partitions
68
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If we have $n$ different kinds of objects...

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#combinatorics #generating-functions
2.5k
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Find the number of ways of making change for a dollar with coins where the number of coins is odd

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#combinatorics #discrete-mathematics #permutations #combinations #generating-functions
140
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Generating function for $a_n=n$, $n\ge0$

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#sequences-and-series #generating-functions
348
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Using generating functions to find number of ways to divide 15 indistinguishable balls into 10 distinguishable non empty cells?

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#combinatorics #generating-functions
456
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Find the coefficient of $x^{17}$ in $(x^2+x^3+x^4+x^5+x^6+x^7+...)^3.$

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#combinatorics #binomial-coefficients #generating-functions
67
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Given the problem : find the coefficient of $x^{100}$ in $\frac{1}{\left(1-x^5\right)\left(1-x^{10}\right)}$, why this solution works?

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#combinatorics #generating-functions
315
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Find the number of solutions of x+y+z=17?

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#combinatorics #generating-functions
2.9k
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Find generating functions given a sequence, and vice versa?

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#combinatorics #discrete-mathematics #power-series #binomial-coefficients #generating-functions

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