List questions from multinomial-coefficients

141

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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 26 Mar 2026 - 14:31

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

156

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I need a combinatorial proof of $\sum_{n_1+n_2+n_3=n} \binom{n}{n_1, n_2,n_3}(-1)^{n_2} = 1$

Published on 23 Oct 2020 - 7:08

85

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Combination with at least n elements

Published on 25 Oct 2020 - 18:15

41

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Bound on function of sum of powers

Published on 26 Oct 2020 - 14:44

28

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How many positive integral solutions exist for $2a+3b-c = 0$ where $a$ ranges from $0$ to $5$, $b$ from $0$ to $10$ and $c$ from $0$ to $40$?

Published on 26 Oct 2020 - 15:58

73

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What is the size of a multinomial?

Published on 24 Feb 2026 - 0:01

93

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Find the coefficient of $x^{12}$ in $(1+x)^{-1}$

Published on 29 Oct 2020 - 21:37

472

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Find coefficient of $x^r$ in $(x^5+x^6+x^7+...)^8$

Published on 30 Oct 2020 - 6:11

1.2k

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How many ways are there to distribute eight different toys among four children if the first child gets at least two toys?

Published on 30 Oct 2020 - 16:57

194

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Number of ways of splitting set into disjoint subsets

Published on 15 Nov 2020 - 12:26

129

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Multiplicity of integer partitions in iterative process

Published on 17 Nov 2020 - 5:07

64

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Multinomial type finite sum

Published on 26 Mar 2026 - 14:26

150

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What is the number of partitions of a set of size $16$ into $4$ subsets of size $4$?

Published on 18 Nov 2020 - 13:33

List Question

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

Negative multinomial expansion

PGF of negative multinomial expansion

I need a combinatorial proof of $\sum_{n_1+n_2+n_3=n} \binom{n}{n_1, n_2,n_3}(-1)^{n_2} = 1$

Combination with at least n elements

Bound on function of sum of powers

How many positive integral solutions exist for $2a+3b-c = 0$ where $a$ ranges from $0$ to $5$, $b$ from $0$ to $10$ and $c$ from $0$ to $40$?

What is the size of a multinomial?

Find the coefficient of $x^{12}$ in $(1+x)^{-1}$

Find coefficient of $x^r$ in $(x^5+x^6+x^7+...)^8$

How many ways are there to distribute eight different toys among four children if the first child gets at least two toys?

Number of ways of splitting set into disjoint subsets

Multiplicity of integer partitions in iterative process

Multinomial type finite sum

What is the number of partitions of a set of size $16$ into $4$ subsets of size $4$?

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