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Placing a kth adjacent term in a row of k-1 non-adjacent terms

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#combinatorics #combinations #generating-functions
185
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Generating Function of Riordan numbers

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#sequences-and-series #combinatorics #discrete-mathematics #generating-functions
62
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Find coefficient in this expression

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#combinatorics #generating-functions
104
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Lyndon words over the binary alphabet that begin with "00"

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#combinatorics #generating-functions #riemann-zeta #oeis #lyndon-words
99
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Closed form for the recursion $g(i,j) = g(i-1,j) + g(i,j-1)$

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#recurrence-relations #generating-functions
94
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Solving homogeneous linear recurrence relation with double non-constant coefficients

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#sequences-and-series #discrete-mathematics #eigenvalues-eigenvectors #recurrence-relations #generating-functions
329
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Converting $ \int_0^{\infty} \frac{e^{-\varepsilon s} \, (s+s^2)^{\beta}}{\log^{\gamma}((1+s)/s)} \, ds$ to a sum?

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#calculus #integration #special-functions #generating-functions #closed-form
325
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Non-crossing Partition

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#combinatorics #discrete-mathematics #recurrence-relations #generating-functions #catalan-numbers
116
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Showing the formal identity $(1-x+x^2)(1-x^2+x^4)(1-x^4+x^8)\cdots =\frac{1}{1+x+x^2}$

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#sequences-and-series #algebra-precalculus #polynomials #generating-functions
69
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Number of different suits among some randomly chosen cards

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#combinatorics #recurrence-relations #expected-value #generating-functions #inclusion-exclusion
66
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Generating function on Lehman's Mathematics for Computer Science

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#generating-functions
37
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Ways of Changing 85/90 dollars

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#generating-functions
36
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random number selection and generating function

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#probability #generating-functions
58
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Generating function and integer sequence that arise from this function

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#combinatorics #power-series #generating-functions #catalan-numbers
540
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Coefficient extraction,show: $[z^n]\frac{1}{(1-z)^{\alpha + 1}} \log \frac{1}{1-z} = \binom{n + \alpha }{n} (H_{n+\alpha} - H_{\alpha})$

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#calculus #algorithms #binomial-coefficients #generating-functions #harmonic-numbers

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