List questions from binomial-coefficients

Published on 11 Apr 2026 - 17:08

246

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Showing that, in Pascal's triangle, the product of the numbers along each median is always the same.

Published on 15 Apr 2026 - 14:51

118

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Show $\sum_{i=0}^n{i\frac{{n \choose i}i!n(2n-1-i)!}{(2n)!}}=\frac{n}{n+1}$

Published on 16 Apr 2026 - 13:40

25

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PGF of a Poisson-binomial

Published on 11 Apr 2026 - 20:11

47

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Find the distribution of $P(X=x \mid X+Y=t)$ and calculate its expected value.

Published on 13 Apr 2026 - 22:23

100

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Does this recursive journey through Pascal's triangle always reach $1$?

Published on 12 Apr 2026 - 4:31

74

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Why is $\sum_{n=0}^{\infty}{ n+1 \choose n }x^{n} = \frac{1}{(1-x)^2}$ when computing recurrences with generating functions?

Published on 15 Apr 2026 - 16:52

32

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Find the first four terms in the binomial series expansion

Published on 11 Apr 2026 - 17:47

207

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$e$ is hidden in Pascal's (binomial) triangle. What is hidden in the trinomial triangle, in the same way?

Published on 11 Apr 2026 - 17:00

65

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How many lattice paths from $(0, 1, 2)$ to $(5, 5, 5)$ that pass through $(3, 3, 3)$ but not $(1, 2, 3)$?

Published on 16 Apr 2026 - 10:24

59

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How to simplify coefficient of Maclaurin series

Published on 08 Apr 2026 - 18:00

42

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Finding particular solution using domain transformation

Published on 09 Apr 2026 - 2:16

61

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Binomial coefficients from a combinatorial point of view

Published on 17 Apr 2026 - 11:43

80

Views

Negative binomial theorem-proof by induction

Published on 11 Apr 2026 - 21:06

82

Views

An identity involving alternative sum of triple product of binomial coefficients

Published on 11 Apr 2026 - 21:33

List Question

Binomial identity?

Showing that, in Pascal's triangle, the product of the numbers along each median is always the same.

Show $\sum_{i=0}^n{i\frac{{n \choose i}i!n(2n-1-i)!}{(2n)!}}=\frac{n}{n+1}$

PGF of a Poisson-binomial

Find the distribution of $P(X=x \mid X+Y=t)$ and calculate its expected value.

Does this recursive journey through Pascal's triangle always reach $1$?

Why is $\sum_{n=0}^{\infty}{ n+1 \choose n }x^{n} = \frac{1}{(1-x)^2}$ when computing recurrences with generating functions?

Find the first four terms in the binomial series expansion

$e$ is hidden in Pascal's (binomial) triangle. What is hidden in the trinomial triangle, in the same way?

How many lattice paths from $(0, 1, 2)$ to $(5, 5, 5)$ that pass through $(3, 3, 3)$ but not $(1, 2, 3)$?

How to simplify coefficient of Maclaurin series

Finding particular solution using domain transformation

Binomial coefficients from a combinatorial point of view

Negative binomial theorem-proof by induction

An identity involving alternative sum of triple product of binomial coefficients

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