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Proof of a generating functions formula

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#sequences-and-series #generating-functions
1.4k
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About the exponential generating function of the involutions of $\mathbb{S}_n$

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#combinatorics #generating-functions #involutions
54
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$ a(n,K) = \sum_{i = 1}^{n-1} i^K a(i,K) a(n-i,K) $?

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#recurrence-relations #asymptotics #generating-functions #closed-form
156
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Calculating a generating function

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#combinatorics #discrete-mathematics #generating-functions
340
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Dirichlet generating function of Möbius function

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#number-theory #generating-functions #riemann-zeta
334
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Generating function of $\log(\log(n))$

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#sequences-and-series #power-series #generating-functions
827
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Finding a function for a sequence that alternates between $0$ and $1$ $\frac{n}{2}$ times?

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#sequences-and-series #generating-functions
543
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Hermite polynomials $H_{n}(y)=\frac{1}{\sqrt{2^n}}\left( y -\frac{d}{dy} \right)^n$ equivalent form

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#functional-analysis #generating-functions #operator-algebras #hermite-polynomials
414
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Sum of dice throws equal to 14

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#probability #generating-functions
268
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Generating function for number of $r$-disjoint subsets each of size $k$

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#probability #combinatorics #generating-functions
388
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Number of solutions to linear diophantine equation in 3 variables

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#elementary-number-theory #diophantine-equations #generating-functions
257
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Riemann Zeta generating function of the sum of divisors.

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#number-theory #generating-functions
598
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Odd values for Dirichlet beta function

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#sequences-and-series #generating-functions #infinite-product #dirichlet-series
401
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How to find generating function that every positive integer can be written as a unique sum of powers of 3

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#combinatorics #generating-functions
914
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Number of integer solutions to linear equation with restrictions

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#combinatorics #permutations #generating-functions

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