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Hillman and Hoggat's Binomial Generalization

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#combinatorics #binomial-coefficients
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Integers in the form $\sum_{j=0}^n a_j2^j3^{n-j}$

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#elementary-number-theory #discrete-mathematics #binomial-coefficients
310
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Find the sum $\sum_{j=0}^{n}\binom{4n}{4j}$

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#algebra-precalculus #binomial-coefficients
137
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Question about Binomial Sums

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#combinatorics #algebra-precalculus #summation #binomial-coefficients #factorial
272
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When $\frac{C(n, k)}{n^{k-1}} > 1$?

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37
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How to find the value of the following items summed up together?

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#binomial-coefficients #combinations
767
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Showing $\binom{2n}{n} = (-4)^n \binom{-1/2}{n}$

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#binomial-coefficients #factorial
130
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Summation with Binomial Coefficients, $\sum (-1)^k \binom{m_1}{k} \binom{m_2}{k} $

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#summation #binomial-coefficients
150
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Evaluate: $\sum_{k=2}^n\frac {n!}{(n-k)!(k-2)!}$

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#summation #binomial-coefficients #factorial
55
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Calculating the sum of a binomial coefficient series

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#combinatorics #binomial-coefficients
150
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What is the coefficient of $x^{17}$ in the formula $(x^2+x)^{15} $?

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#combinatorics #discrete-mathematics #binomial-coefficients
47
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sum of a binomial coefficient

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#combinatorics #discrete-mathematics #binomial-coefficients
54
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What is the smallest value beside 1 of a binomial with two integer values > 0?

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#binomial-coefficients
397
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Binomial coefficients and cosin

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#trigonometry #binomial-coefficients #binomial-theorem
99
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On ${-1 \choose 0}=1$, can I assume that $\frac{(-1)!}{(-1)!}=1$?

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