List questions from multinomial-theorem

140

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How to find the coefficient of $x^{l}$ in the expansion of $(1+x+x^{2}+...+x^{n})^{m}$ for some given $l$?

Published on 15 Oct 2020 - 1:25

59

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$a_{m, n}$ is coefficient of $x^n$ in expansion $(1+x+x^2)^m.$ Prove $0\leq \sum_{i = 0}^{\left\lfloor 2k/3\right\rfloor} (-1)^ia_{k-i,i} \leq 1$

Published on 16 Oct 2020 - 14:43

68

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Why do we divide by the count of each letter in questions of the form "how many words can I form from the letters in"?

Published on 17 Oct 2020 - 21:33

116

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Negative multinomial expansion

Published on 23 Feb 2026 - 23:57

136

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PGF of negative multinomial expansion

Published on 23 Feb 2026 - 23:58

73

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What is the size of a multinomial?

Published on 24 Feb 2026 - 0:01

63

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Multinomial type finite sum

Published on 18 Nov 2020 - 1:12

232

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Proof of Sum of Trinomial Coeffs = $3^n$

Published on 24 Nov 2020 - 23:40

81

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Application of multinominal theorem for a tricky sum

Published on 27 Nov 2020 - 20:53

27

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What is the asymptotic growth of the terms in this expression?

Published on 28 Nov 2020 - 14:47

73

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Prove that ${a_{1} +2a_{2} +3a_{3}+\cdots+np\ a_{n}}_{p} \ =\frac{np}{2}( 1+p)^{n}$

Published on 02 Dec 2020 - 7:33

68

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Why is $P(X=x, Y=y, Z=z)$ = $\frac{n!}{x!y!z!}$?

Published on 29 Dec 2020 - 16:45

65

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How many rational elements are in the multinomial? $(\sqrt[3]{x}+\sqrt[5]{x}+2\sqrt{x})^5$

Published on 05 Jan 2021 - 21:47

110

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Can the following expression be related to the multinomial formula?

Published on 28 Jan 2021 - 19:39

174

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The $q$ Multilinear Theorem

Published on 25 Mar 2026 - 19:00

List Question

How to find the coefficient of $x^{l}$ in the expansion of $(1+x+x^{2}+...+x^{n})^{m}$ for some given $l$?

$a_{m, n}$ is coefficient of $x^n$ in expansion $(1+x+x^2)^m.$ Prove $0\leq \sum_{i = 0}^{\left\lfloor 2k/3\right\rfloor} (-1)^ia_{k-i,i} \leq 1$

Why do we divide by the count of each letter in questions of the form "how many words can I form from the letters in"?

Negative multinomial expansion

PGF of negative multinomial expansion

What is the size of a multinomial?

Multinomial type finite sum

Proof of Sum of Trinomial Coeffs = $3^n$

Application of multinominal theorem for a tricky sum

What is the asymptotic growth of the terms in this expression?

Prove that ${a_{1} +2a_{2} +3a_{3}+\cdots+np\ a_{n}}_{p} \ =\frac{np}{2}( 1+p)^{n}$

Why is $P(X=x, Y=y, Z=z)$ = $\frac{n!}{x!y!z!}$?

How many rational elements are in the multinomial? $(\sqrt[3]{x}+\sqrt[5]{x}+2\sqrt{x})^5$

Can the following expression be related to the multinomial formula?

The $q$ Multilinear Theorem

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