Question

Serge Lang's Basic Mathematics: Binomial Coefficiants

score 103 · Answer 1 · 2026-04-15 12:59:19

103

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Serge Lang's Basic Mathematics: Binomial Coefficiants

Published on 15 Apr 2026 - 12:59

score 30 · Answer 2 · 2026-04-14 14:47:22

30

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Choosing k positions among n with no more distance d each other

Published on 14 Apr 2026 - 14:47

score 737 · Answer 3 · 2026-04-13 23:02:22

737

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Does the interior of Pascal's triangle contain three consecutive integers?

Published on 13 Apr 2026 - 23:02

score 27 · Answer 4 · 2026-04-14 04:37:37

27

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Binomial Coefficient Bounded by Polynomial Decay

Published on 14 Apr 2026 - 4:37

score 179 · Answer 5 · 2026-04-15 16:27:17

179

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The polynomial P(x) is equal to $(i + x)^{2024}$. Let $S$ be the sum of all the real coefficients of $P(x)$. Find $\log_{2} S$.

Published on 15 Apr 2026 - 16:27

score 44 · Answer 6 · 2026-04-13 23:39:50

44

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Convergence of sequence including binomial coefficients

Published on 13 Apr 2026 - 23:39

score 709 · Answer 7 · 2026-04-12 17:33:20

709

Views

I tried to kill the central binomial coefficients, but they came back.

Published on 12 Apr 2026 - 17:33

score 40 · Answer 8 · 2026-03-25 09:33:52

40

Views

Rewriting summation in binomial form - counting problem

Published on 25 Mar 2026 - 9:33

score 27 · Answer 9 · 2026-03-26 07:57:02

27

Views

Weighted sum of specific multinomial coefficients

Published on 26 Mar 2026 - 7:57

score 49 · Answer 10 · 2026-04-15 10:34:25

49

Views

How can you derermine if you are allowed to use use 0^0=1 in this proof?

Published on 15 Apr 2026 - 10:34

score 294 · Answer 11 · 2026-04-17 01:28:37

294

Views

Regarding Egorychev integrals for binomial coefficients

Published on 17 Apr 2026 - 1:28

score 86 · Answer 12 · 2026-04-13 19:58:06

86

Views

Summation coming about in the process of solving a 3d random walk $\sum\limits_{i=0}^n {n \choose i}^2 {2(n-i)\choose (n-i)}$

Published on 13 Apr 2026 - 19:58

score 119 · Answer 13 · 2026-03-26 08:00:33

119

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Prove $\sum_k{{a+b \choose a+k}{b+c \choose b+k}{c+a \choose c+k}(-1)^k}=\dfrac{(a+b+c)!}{a!b!c!}$

Published on 26 Mar 2026 - 8:00

score 657 · Answer 14 · 2026-04-13 02:41:46

657

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Conjecture: In Pascal's triangle with $n$ rows, the proportion of numbers less than the centre number approaches $e^{-1/\pi}$ as $n\to\infty$.

Published on 13 Apr 2026 - 2:41

score 116 · Answer 15 · 2026-04-16 06:26:10

116

Views

Generalization of binomial coefficients to both non-integer arguments

Published on 16 Apr 2026 - 6:26

List Question

Serge Lang's Basic Mathematics: Binomial Coefficiants

Choosing k positions among n with no more distance d each other

Does the interior of Pascal's triangle contain three consecutive integers?

Binomial Coefficient Bounded by Polynomial Decay

The polynomial P(x) is equal to $(i + x)^{2024}$. Let $S$ be the sum of all the real coefficients of $P(x)$. Find $\log_{2} S$.

Convergence of sequence including binomial coefficients

I tried to kill the central binomial coefficients, but they came back.

Rewriting summation in binomial form - counting problem

Weighted sum of specific multinomial coefficients

How can you derermine if you are allowed to use use 0^0=1 in this proof?

Regarding Egorychev integrals for binomial coefficients

Summation coming about in the process of solving a 3d random walk $\sum\limits_{i=0}^n {n \choose i}^2 {2(n-i)\choose (n-i)}$

Prove $\sum_k{{a+b \choose a+k}{b+c \choose b+k}{c+a \choose c+k}(-1)^k}=\dfrac{(a+b+c)!}{a!b!c!}$

Conjecture: In Pascal's triangle with $n$ rows, the proportion of numbers less than the centre number approaches $e^{-1/\pi}$ as $n\to\infty$.

Generalization of binomial coefficients to both non-integer arguments

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