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Evaluating the function $S(a) = \sum_{n=0}^{\infty} a^n \binom{2n}{n}.$

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#sequences-and-series #combinatorics #binomial-coefficients
31
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Expanding an algebraic expression that is a product of linear expressions to powers

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#abstract-algebra #algebra-precalculus #binomial-coefficients
39
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When proving $\binom{n}{r} = \binom{n-1}{r} + \binom{n-1}{r-1}$ per induction over $n$, why don’t we need induction over $r$?

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#induction #binomial-coefficients #binomial-theorem
209
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Binomial coefficient modulo

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#binomial-coefficients
353
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Dissecting the complexity of prime numbers

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#combinatorics #number-theory #reference-request #prime-numbers #binomial-coefficients
101
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Binomial sum formula for $(n+1)^{n-1}$

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#binomial-coefficients
179
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Sum of alternating ratio of combinations

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#combinatorics #binomial-coefficients #combinations #upper-lower-bounds
134
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Asymptotic approximation of the expression $\sum _{i=0}^n \log (\binom{n}{i}+1)$

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#summation #asymptotics #binomial-coefficients #approximation
1.5k
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Expressing polynomials as binomial coefficients

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#combinatorics #polynomials #binomial-coefficients
524
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A conjecture about big prime numbers

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#combinatorics #number-theory #prime-numbers #binomial-coefficients
122
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Asymptotic approximation of the expression $\sum^{N}_{i=0}\log\Bigg[\binom{\binom{N+1}{i}}{t_i}\Bigg]$

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#summation #asymptotics #binomial-coefficients #approximation
90
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An expression involving trig functions and binomial coefficients

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#trigonometry #binomial-coefficients
101
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is the right approach to use the binary entropy function to get a $O(c^n)$ approximation?

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#combinatorics #discrete-mathematics #algorithms #binomial-coefficients
192
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Series of binomial coefficient denominators

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#sequences-and-series #binomial-coefficients #closed-form #hypergeometric-function #beta-function
2.2k
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Bernoulli trials (n,p) - probability for even/odd number of successes

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#probability #combinatorics #probability-theory #binomial-coefficients #combinations

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