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Binomial Coefficient Solve for n Where $_{20} C_{n+2} = _{20} C_{ 2n-1} $

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#probability #statistics #binomial-coefficients
271
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Show that $ \sum_{k=0}^{j} \binom{2j+1}{k+j+1} \ \frac{(-1)^k}{2k+1}=2^{2j-1}\ B(j+1,1/2)$.

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#sequences-and-series #binomial-coefficients #divergent-series #beta-function
1k
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Binomial summation $\sum\binom nkk^2$

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#combinatorics #summation #binomial-coefficients #generating-functions
85
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Binomial summation with alternating terms?

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#summation #binomial-coefficients
51
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Proving a sum that equals $y!/((y-z)\cdots(1-z))$

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#summation #binomial-coefficients
48
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Summation of partial products

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#summation #binomial-coefficients #generating-functions
1.7k
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How to find the coefficient of $x^{203}$ in the expansion of $(x-1)(x^2 - 2)(x^3-3)\dots(x^{20} - 20)$?

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#binomial-coefficients
1k
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Bijection for $q$-binomial coefficient

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#combinatorics #binomial-coefficients #integer-partitions #q-analogs
441
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Confusion about proof involving sums and binomial coefficients

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#summation #binomial-coefficients #proof-explanation
35
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Prove $\binom{n}{1} - \frac{1}{2}\binom{n}{2} + \frac{1}{3}\binom{n}{3} + \ldots = 1 + \frac{1}{2} + \frac{1}{3} + \ldots + \frac{1}{n}$

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#sequences-and-series #summation #binomial-coefficients
1.1k
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Finding coefficient of $x^n$ in $(1-9x+20x^2)^{-1}$.

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#binomial-coefficients #binomial-theorem
460
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How many triangles can be formed in a 4 x 3 rectangle?

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#binomial-coefficients
1k
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Inequality with Sum of Binomial Coefficients

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#inequality #asymptotics #binomial-coefficients
399
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Comparing Coefficients?

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#binomial-coefficients
759
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Triangle inequality raised to fractional powers

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#linear-algebra #polynomials #binomial-coefficients

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