List questions from binomial-coefficients

Published on 15 Apr 2026 - 23:22

61

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Finding $B_k$, if $ (1+x-x^2)^n=\sum_{k=0}^{2n} B_k x^k$

Published on 16 Apr 2026 - 2:44

184

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Value of $\sum_{k=0}^n \binom{n}{k}^2$ using analysis.

Published on 11 Apr 2026 - 0:55

42

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Two forms of $B_k$, if $(1+x-x^2)^n=\sum_{k=0}^{2n} B_k x^k$

Published on 16 Apr 2026 - 12:02

212

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Approximating a sum of products of binomial coefficients

Published on 12 Apr 2026 - 21:12

199

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Find $\sum^{n}_{k=1} \binom{n}{k} \frac{(-1)^k}{k^a}$

Published on 15 Apr 2026 - 8:22

112

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A sequence defined by $(2^n-1)\,a_n=\sum_{k=1}^n\binom n k\,a_{n-k}\,(k+1)^{-1}$

Published on 15 Apr 2026 - 23:19

82

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How does the binomial coefficient relate to the combinations formula?

Published on 09 Apr 2026 - 9:39

344

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Polynomial representation of $\sum\limits_{n=m+1}^N \binom {n-1} m$

Published on 13 Apr 2026 - 20:51

31

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Where Error in evaluate summmation :$\sum_{k=0}^{m}\binom{n-k}{m-k}$

Published on 15 Apr 2026 - 20:38

68

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Exponential generating function of binomial coefficients in pascal's triangle

Published on 11 Apr 2026 - 12:48

64

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Deriving a general formula for the nth composition of a function

Published on 12 Apr 2026 - 8:21

39

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Sum of a binomial relation confusion

Published on 26 Mar 2026 - 2:54

36

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Prove that $\sum_{r=1}^n (-1)^{r-1}(1+\frac{1}{2}+\frac{1}{3}+...\frac{1}{r}) \binom{n}{r} =\frac{1}{n}$.

Published on 16 Apr 2026 - 4:44

78

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What is the most efficient way to find the coefficient before the $n$-th term in this generating function?

Published on 25 Mar 2026 - 7:49

List Question

Alternating hockey stick sum $\sum_{m=k}^M (-1)^m \binom{m}{k}$

Finding $B_k$, if $ (1+x-x^2)^n=\sum_{k=0}^{2n} B_k x^k$

Value of $\sum_{k=0}^n \binom{n}{k}^2$ using analysis.

Two forms of $B_k$, if $(1+x-x^2)^n=\sum_{k=0}^{2n} B_k x^k$

Approximating a sum of products of binomial coefficients

Find $\sum^{n}_{k=1} \binom{n}{k} \frac{(-1)^k}{k^a}$

A sequence defined by $(2^n-1)\,a_n=\sum_{k=1}^n\binom n k\,a_{n-k}\,(k+1)^{-1}$

How does the binomial coefficient relate to the combinations formula?

Polynomial representation of $\sum\limits_{n=m+1}^N \binom {n-1} m$

Where Error in evaluate summmation :$\sum_{k=0}^{m}\binom{n-k}{m-k}$

Exponential generating function of binomial coefficients in pascal's triangle

Deriving a general formula for the nth composition of a function

Sum of a binomial relation confusion

Prove that $\sum_{r=1}^n (-1)^{r-1}(1+\frac{1}{2}+\frac{1}{3}+...\frac{1}{r}) \binom{n}{r} =\frac{1}{n}$.

What is the most efficient way to find the coefficient before the $n$-th term in this generating function?

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