List questions from binomial-coefficients

Published on 17 Apr 2026 - 10:51

105

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How to prove that $(a+b)!/a!b!$ is an integer

Published on 13 Apr 2026 - 20:44

64

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Simplifying a series with multiset coefficients

Published on 26 Mar 2026 - 4:28

59

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Lattice path back at origin explanation

Published on 08 Apr 2026 - 6:27

54

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Determinant of matrix of binomial coefficients

Published on 14 Apr 2026 - 4:10

49

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Property about the alternating Pascal triangle

Published on 10 Apr 2026 - 17:38

105

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Sum of multinomial coefficient

Published on 26 Mar 2026 - 6:19

58

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$f_n(ab) = f_n(a)f_n(b) + f_n(a-1)f_n(b-1) + f_n(a-2)f_n(b-2)+ ...+f_n(a-n)f_n(b-n)$

Published on 16 Apr 2026 - 20:04

198

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Alternating sign Vandermonde convolution like quantity

Published on 15 Apr 2026 - 13:18

271

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On the binomial coefficient $\binom{-1}{-1}$

Published on 17 Apr 2026 - 4:23

166

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Prove combination of polynomials must be odd polynomials with positive coefficients.

Published on 16 Apr 2026 - 23:16

96

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Why if $a_n=-n\sum_{m=1}^{n}\frac{(-1)^{m}}{m}\binom{m+n-1}{2m-1}b_m$ then $b_m = \sum_{n=1}^{m}(-1)^{n+1}\binom{2m}{m-n}a_n?$

Published on 17 Apr 2026 - 17:47

21

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Finding the coefficients $c_n$ in the expression $x^m \phi_{n_0} = \sum_n c_n \phi_n$, where $\phi_n$ is a Hermite function

Published on 25 Mar 2026 - 11:33

89

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Asymtotic of some binomial sum

Published on 11 Apr 2026 - 10:54

136

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Double summation with binomial coefficients

Published on 17 Apr 2026 - 5:25

List Question

I need combinatorial proof for the following expression

How to prove that $(a+b)!/a!b!$ is an integer

Simplifying a series with multiset coefficients

Lattice path back at origin explanation

Determinant of matrix of binomial coefficients

Property about the alternating Pascal triangle

Sum of multinomial coefficient

$f_n(ab) = f_n(a)f_n(b) + f_n(a-1)f_n(b-1) + f_n(a-2)f_n(b-2)+ ...+f_n(a-n)f_n(b-n)$

Alternating sign Vandermonde convolution like quantity

On the binomial coefficient $\binom{-1}{-1}$

Prove combination of polynomials must be odd polynomials with positive coefficients.

Why if $a_n=-n\sum_{m=1}^{n}\frac{(-1)^{m}}{m}\binom{m+n-1}{2m-1}b_m$ then $b_m = \sum_{n=1}^{m}(-1)^{n+1}\binom{2m}{m-n}a_n?$

Finding the coefficients $c_n$ in the expression $x^m \phi_{n_0} = \sum_n c_n \phi_n$, where $\phi_n$ is a Hermite function

Asymtotic of some binomial sum

Double summation with binomial coefficients

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