List questions from binomial-coefficients

Published on 08 Feb 2019 - 0:36

47

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Is the following equation valid for a binomial coefficient?

Published on 25 Mar 2026 - 23:16

521

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Prove that $4^n>{2n\choose n}$ [other version: $(2n!)<2^{2n}(n!)^2$]

Published on 08 Feb 2019 - 13:27

106

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Rigorous or not?

Published on 26 Mar 2026 - 9:44

3.8k

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Prove by induction: $C(2n, 2) = 2C(n, 2) + n^2$

Published on 08 Feb 2019 - 22:29

42

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How to prove $\sum_{1 < k < n}\binom{n-k}{1}\binom{k-1}{t+1} = \binom{n}{t+3}$?

Published on 09 Feb 2019 - 12:46

62

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Is this the correct notation for a binomial coefficient?

Published on 09 Feb 2019 - 23:05

2.7k

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Infinite binomial sum

Published on 27 Mar 2026 - 6:06

29

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How is the Combinatorial proof derived?

Published on 10 Feb 2019 - 19:58

58

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Proof of the orthogonality of a given matrix which involves binomial coefficients

Published on 27 Mar 2026 - 3:58

66

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value of $f(2019)$ in binomial expression

Published on 11 Feb 2019 - 7:57

54

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How to complete this proof involving factorials

Published on 26 Mar 2026 - 12:06

50

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Limit of a ratio of two similar binomial coefficients with two variables

Published on 11 Feb 2019 - 23:44

185

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How can I find the coefficient of $x^6$ in $(1+x+\frac{x^2}{2})^{10}$ efficiently with combinatorics?

Published on 25 Mar 2026 - 11:04

86

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When will $f(i):=\binom{2k-1}{i}\Big((1-p)^i(1+p)^{2k-1-i}-(1+p)^i(1-p)^{2k-1-i} \Big)$ attain maximum?

Published on 26 Mar 2026 - 8:02

List Question

Summation of hypergeometric probability multiplied by some factor

Is the following equation valid for a binomial coefficient?

Prove that $4^n>{2n\choose n}$ [other version: $(2n!)<2^{2n}(n!)^2$]

Rigorous or not?

Prove by induction: $C(2n, 2) = 2C(n, 2) + n^2$

How to prove $\sum_{1 < k < n}\binom{n-k}{1}\binom{k-1}{t+1} = \binom{n}{t+3}$?

Is this the correct notation for a binomial coefficient?

Infinite binomial sum

How is the Combinatorial proof derived?

Proof of the orthogonality of a given matrix which involves binomial coefficients

value of $f(2019)$ in binomial expression

How to complete this proof involving factorials

Limit of a ratio of two similar binomial coefficients with two variables

How can I find the coefficient of $x^6$ in $(1+x+\frac{x^2}{2})^{10}$ efficiently with combinatorics?

When will $f(i):=\binom{2k-1}{i}\Big((1-p)^i(1+p)^{2k-1-i}-(1+p)^i(1-p)^{2k-1-i} \Big)$ attain maximum?

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