List questions from binomial-coefficients

Published on 12 Apr 2026 - 12:36

3.2k

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Coefficient of $x^5$ in $(1+x)^{21} + (1+x)^{22} + ... + (1+x)^{30}$

Published on 27 Oct 2016 - 5:03

54

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Calculate the value of sum for any given n

Published on 08 Apr 2026 - 1:28

111

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Find the number of solutions?

Published on 03 Apr 2026 - 2:42

127

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Alternating sum involving binomial coefficient

Published on 08 Apr 2026 - 21:43

506

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coefficient of $x^{2012}$ in $\frac{1+x}{(1+x^2)(1-x)}$

Published on 27 Oct 2016 - 23:01

181

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Prove combinatorial identity using coloring

Published on 28 Oct 2016 - 4:15

98

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Determine if algorithm is infinite for the pair of positive integers $(n,m)$

Published on 12 Apr 2026 - 1:31

813

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Summation of Central Binomial Coefficients divided by even powers of $2$

Published on 29 Oct 2016 - 6:03

1.3k

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Binomial Coefficients with fractions: $\binom {m-\frac 12}m=\frac 1{2^{2m}}\binom {2m}m$.

Published on 29 Oct 2016 - 17:50

350

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Express $11!$ and $\binom{23}{11}$ as products of their prime factors

Published on 09 Apr 2026 - 21:18

3k

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Probability of winning a prize in a raffle (each person can only win once)

Published on 02 Apr 2026 - 18:10

46

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Divisor Problem

Published on 12 Apr 2026 - 0:33

944

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Find coefficient of ordinary generating function

Published on 03 Apr 2026 - 2:32

415

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Prove that $\gcd{\left(\binom M1,\binom M2,\binom M3,\ldots,\binom Mn\right)}=1$ where $M=\mathrm{lcm}(1,2,3,\ldots,n)$

Published on 30 Mar 2026 - 7:26

List Question

Find the close form of a summation with binomial coefficients and fractions

Coefficient of $x^5$ in $(1+x)^{21} + (1+x)^{22} + ... + (1+x)^{30}$

Calculate the value of sum for any given n

Find the number of solutions?

Alternating sum involving binomial coefficient

coefficient of $x^{2012}$ in $\frac{1+x}{(1+x^2)(1-x)}$

Prove combinatorial identity using coloring

Determine if algorithm is infinite for the pair of positive integers $(n,m)$

Summation of Central Binomial Coefficients divided by even powers of $2$

Binomial Coefficients with fractions: $\binom {m-\frac 12}m=\frac 1{2^{2m}}\binom {2m}m$.

Express $11!$ and $\binom{23}{11}$ as products of their prime factors

Probability of winning a prize in a raffle (each person can only win once)

Divisor Problem

Find coefficient of ordinary generating function

Prove that $\gcd{\left(\binom M1,\binom M2,\binom M3,\ldots,\binom Mn\right)}=1$ where $M=\mathrm{lcm}(1,2,3,\ldots,n)$

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