Question

A multinomial theorem for polynomials of one variable

score 216 · Answer 1 · 2023-06-08 14:07:30

216

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A multinomial theorem for polynomials of one variable

Published on 08 Jun 2023 - 14:07

score 61 · Answer 2 · 2023-09-02 22:32:48

61

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When not to use $\binom{n + r − 1} {r− 1}$?

Published on 02 Sep 2023 - 22:32

score 118 · Answer 3 · 2026-03-24 08:36:21

118

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In the multinomial expansion of $(a+b+c+d)^8$, how many terms (monomials) have coefficient $\begin{pmatrix} 8 \\ 2,4,0,2\end{pmatrix}$?

Published on 24 Mar 2026 - 8:36

score 288 · Answer 4 · 2023-09-18 08:27:27

288

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Five different games are to be distributed among $4$ children randomly. The probability that each child get at least one game is?

Published on 18 Sep 2023 - 8:27

score 216 · Answer 5 · 2023-09-19 21:45:46

216

Views

The proof by induction of the multinomial theorem

Published on 19 Sep 2023 - 21:45

score 97 · Answer 6 · 2026-03-24 01:14:51

97

Views

Multinomial theorem for a power series

Published on 24 Mar 2026 - 1:14

score 99 · Answer 7 · 2026-03-24 12:13:16

99

Views

Central Binomial Coefficients and Multinomial Coefficients

Published on 24 Mar 2026 - 12:13

score 136 · Answer 8 · 2023-10-25 11:58:45

136

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Proving the Number Theory Property: $\delta(n^k) = \delta(\delta(n)^k)$ for natural $n$ and $k$

Published on 25 Oct 2023 - 11:58

score 51 · Answer 9 · 2023-12-03 11:06:09

51

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Multinomial Theorem expansion in Combinations Problem

Published on 03 Dec 2023 - 11:06

score 107 · Answer 10 · 2023-12-11 08:02:42

107

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$(1+2x+3x^2)^{50}=a_{0}+ a_{1}x+ ... +a_{100}x^{100}$ Find ratio between $a_{51}$ and $a_{49}$.

Published on 11 Dec 2023 - 8:02

score 77 · Answer 11 · 2026-03-23 05:33:05

77

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If $(1+px+x^2)^n=1+a_{1}x+a_{2} x^2+....+a_{2n}x^{2n}$, then prove that $(np-pr)a_{r}=(r+1)a_{r+1}+(r-1-2n)a_{r-1}$ for $1<r<2n$

Published on 23 Mar 2026 - 5:33

score 328 · Answer 12 · 2024-01-10 23:19:23

328

Views

Why do Bell Polynomial coefficients show up here?

Published on 10 Jan 2024 - 23:19

score 75 · Answer 13 · 2024-02-05 19:58:13

75

Views

Showing the quintessential logarithm property using the Maclaurin series of $\log$

Published on 05 Feb 2024 - 19:58

score 72 · Answer 14 · 2024-02-17 11:27:43

72

Views

Number of monotonically increasing functions such that $f(i)\le i$.

Published on 17 Feb 2024 - 11:27

score 76 · Answer 15 · 2024-02-29 10:44:31

76

Views

Number of integral solutions for $x_1 + x_2 - x_3 = n$ where $n \geq x_1 , x_2 , x_3 \geq 0$

Published on 29 Feb 2024 - 10:44

List Question

A multinomial theorem for polynomials of one variable

When not to use $\binom{n + r − 1} {r− 1}$?

In the multinomial expansion of $(a+b+c+d)^8$, how many terms (monomials) have coefficient $\begin{pmatrix} 8 \\ 2,4,0,2\end{pmatrix}$?

Five different games are to be distributed among $4$ children randomly. The probability that each child get at least one game is?

The proof by induction of the multinomial theorem

Multinomial theorem for a power series

Central Binomial Coefficients and Multinomial Coefficients

Proving the Number Theory Property: $\delta(n^k) = \delta(\delta(n)^k)$ for natural $n$ and $k$

Multinomial Theorem expansion in Combinations Problem

$(1+2x+3x^2)^{50}=a_{0}+ a_{1}x+ ... +a_{100}x^{100}$ Find ratio between $a_{51}$ and $a_{49}$.

If $(1+px+x^2)^n=1+a_{1}x+a_{2} x^2+....+a_{2n}x^{2n}$, then prove that $(np-pr)a_{r}=(r+1)a_{r+1}+(r-1-2n)a_{r-1}$ for $1<r<2n$

Why do Bell Polynomial coefficients show up here?

Showing the quintessential logarithm property using the Maclaurin series of $\log$

Number of monotonically increasing functions such that $f(i)\le i$.

Number of integral solutions for $x_1 + x_2 - x_3 = n$ where $n \geq x_1 , x_2 , x_3 \geq 0$

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