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Asymptotics of Binomial coefficients

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#asymptotics #binomial-coefficients #analytic-combinatorics
291
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A combinatorial sum and identity involving Stirling numbers of the second kind

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#combinatorics #analysis #analytic-number-theory #stirling-numbers #analytic-combinatorics
1.4k
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In how many bit strings of length 10 are there with no 3 0s adjacent

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#combinatorics #analytic-combinatorics
1.3k
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Using generating functions to answer how many bit strings of length N have no 000

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#combinatorics #generating-functions #analytic-combinatorics
46
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Limiting behaviour of usual lengths of runs

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#combinatorics #analytic-combinatorics
528
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Taylor series for multivalued complex functions (and their use in combinatorics)

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#combinatorics #complex-analysis #taylor-expansion #generating-functions #analytic-combinatorics
257
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Generalizing the growth of sums of two squares

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#number-theory #prime-numbers #asymptotics #diophantine-equations #analytic-combinatorics
930
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Lower Bound for Sum.

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#real-analysis #summation #binomial-coefficients #hypergeometric-function #analytic-combinatorics
51
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5 power k in binary form 1's and 0's density for large k.

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#number-theory #analytic-number-theory #analytic-combinatorics
114
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A summation including binomial coefficients

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#sequences-and-series #combinatorics #summation #binomial-coefficients #analytic-combinatorics
251
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closed form expression for the summation $\sum_{i=0}^{\infty}\binom{i+k}{i}x^ii^t$

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#sequences-and-series #derivatives #binomial-coefficients #stirling-numbers #analytic-combinatorics
131
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Bounding integrals using asymptotic expansions of the integrand

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#complex-analysis #singularity #bounds-of-integration #analytic-combinatorics
219
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Prove that $\sum\limits_{j=0}^k\,j\,\binom{n}{j}\,\binom{n-j}{2k-2j}\,2^{2k-2j}=n\binom{2n-2}{2k-2}$

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#combinatorics #summation #binomial-coefficients #analytic-combinatorics
225
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Using the Faà di Bruno formula

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#calculus #combinatorics #derivatives #algorithms #analytic-combinatorics
137
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Deriving exponential generating function for central trinomial coefficients

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#sequences-and-series #combinatorics #special-functions #generating-functions #analytic-combinatorics

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