Question

How do we label/enumerate binomial-coefficient-many objects explicitly? (light question)

score 153 · Answer 1 · 2020-01-24 11:30:24

153

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How do we label/enumerate binomial-coefficient-many objects explicitly? (light question)

Published on 24 Jan 2020 - 11:30

score 68 · Answer 2 · 2020-01-25 04:23:41

68

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1•²⁵C₀ + 5•²⁵C₁ + 9•²⁵C₂ ..... 101•²⁵C₂₅ = 2²⁵ • k. Find the value of k.

Published on 25 Jan 2020 - 4:23

score 37 · Answer 3 · 2026-04-01 11:19:39

37

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Coefficients for Polynomials Giving Number of Paths of an LR Grid

Published on 01 Apr 2026 - 11:19

score 132 · Answer 4 · 2026-03-29 21:13:27

132

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Binomial expansions of index

Published on 29 Mar 2026 - 21:13

score 108 · Answer 5 · 2026-03-25 09:27:01

108

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On a sum of binomial coefficients and inequalities

Published on 25 Mar 2026 - 9:27

score 101 · Answer 6 · 2020-01-27 13:38:24

101

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On summation $\sum_{k = 0}^n \binom nk^2 x^k y^{n-k} $

Published on 27 Jan 2020 - 13:38

score 52 · Answer 7 · 2026-03-29 21:14:55

52

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If $\sum_{0}^{2n}a_r(x-2)^r=\sum_{0}^{2n}b_r(x-3)^r$ and $a_k=1$ $\forall$ $k\ge n$, then show that $b_n=\displaystyle{2n+1\choose n+1}$

Published on 29 Mar 2026 - 21:14

score 206 · Answer 8 · 2026-03-29 21:21:03

206

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Prove that $\dfrac{72!}{(36!)^2}-1$ is divisible by $73$

Published on 29 Mar 2026 - 21:21

score 108 · Answer 9 · 2026-03-25 14:27:31

108

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New wrong recurrence formula for Bell numbers

Published on 25 Mar 2026 - 14:27

score 732 · Answer 10 · 2026-03-26 06:20:19

732

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A combinatorial identity - Hockey Stick generalization

Published on 26 Mar 2026 - 6:20

score 258 · Answer 11 · 2020-01-29 12:45:32

258

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choosing two pairs from a set such that the pairs are not the same thing

Published on 29 Jan 2020 - 12:45

score 118 · Answer 12 · 2026-03-26 22:13:44

118

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Formula for $\sum_{k=0}^n {n \choose k}^4$

Published on 26 Mar 2026 - 22:13

score 114 · Answer 13 · 2026-03-11 05:19:42

114

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Number of preorder relations on a set related to the open problem about preorder relations

Published on 11 Mar 2026 - 5:19

score 62 · Answer 14 · 2026-03-27 18:05:06

62

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Probability that two slices of cake have an equal number of raisins

Published on 27 Mar 2026 - 18:05

score 178 · Answer 15 · 2026-03-26 22:14:02

178

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Simplifying $\binom{n}{0} - \binom{n}{1} + \binom{n}{2} - \binom{n}{3} + \cdots + (-1)^n \binom{n}{n}$

Published on 26 Mar 2026 - 22:14

List Question

How do we label/enumerate binomial-coefficient-many objects explicitly? (light question)

1•²⁵C₀ + 5•²⁵C₁ + 9•²⁵C₂ ..... 101•²⁵C₂₅ = 2²⁵ • k. Find the value of k.

Coefficients for Polynomials Giving Number of Paths of an LR Grid

Binomial expansions of index

On a sum of binomial coefficients and inequalities

On summation $\sum_{k = 0}^n \binom nk^2 x^k y^{n-k} $

If $\sum_{0}^{2n}a_r(x-2)^r=\sum_{0}^{2n}b_r(x-3)^r$ and $a_k=1$ $\forall$ $k\ge n$, then show that $b_n=\displaystyle{2n+1\choose n+1}$

Prove that $\dfrac{72!}{(36!)^2}-1$ is divisible by $73$

New wrong recurrence formula for Bell numbers

A combinatorial identity - Hockey Stick generalization

choosing two pairs from a set such that the pairs are not the same thing

Formula for $\sum_{k=0}^n {n \choose k}^4$

Number of preorder relations on a set related to the open problem about preorder relations

Probability that two slices of cake have an equal number of raisins

Simplifying $\binom{n}{0} - \binom{n}{1} + \binom{n}{2} - \binom{n}{3} + \cdots + (-1)^n \binom{n}{n}$

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