Question

How do you prove that $\binom{n}{d} = \Theta(n^d)$?

score 154 · Answer 1 · 2019-04-02 07:44:01

154

Views

How do you prove that $\binom{n}{d} = \Theta(n^d)$?

Published on 02 Apr 2019 - 7:44

score 538 · Answer 2 · 2026-03-26 15:16:45

538

Views

Some clarifications about Pascal's rule needed.

Published on 26 Mar 2026 - 15:16

score 158 · Answer 3 · 2019-04-03 10:46:58

158

Views

General Leibniz's rule, why cases k=0 and k=n are separated from the sum?

Published on 03 Apr 2019 - 10:46

score 65 · Answer 4 · 2019-04-03 11:49:35

65

Views

$ {q \choose m} = 0$, for all $m = 1, ..., q-1$.

Published on 03 Apr 2019 - 11:49

score 99 · Answer 5 · 2019-04-04 05:11:10

99

Views

Verify the coefficient of $x^n$ from expansion is $\binom{2n+1}{n}$

Published on 04 Apr 2019 - 5:11

score 44 · Answer 6 · 2026-03-26 14:20:58

44

Views

Distribute m=17 cards to n=7 entities

Published on 26 Mar 2026 - 14:20

score 343 · Answer 7 · 2019-04-04 14:28:25

343

Views

Pascal triangle with more numbers to add

Published on 04 Apr 2019 - 14:28

score 193 · Answer 8 · 2019-04-04 18:16:25

193

Views

Calculate $\sum_{0 \le k } \binom{n+k}{2k} \binom{2k}{k} \frac{(-1)^k}{k+1}$

Published on 04 Apr 2019 - 18:16

score 532 · Answer 9 · 2019-04-04 18:58:36

532

Views

Find the coefficient of a term in the expansion of an algebraic expression

Published on 04 Apr 2019 - 18:58

score 135 · Answer 10 · 2026-03-27 15:18:57

135

Views

If $C_0, C_1, C_2, .., C_n$ are the binomial coefficients in the expansion of $(1+x)^n$

Published on 27 Mar 2026 - 15:18

score 219 · Answer 11 · 2026-03-27 15:19:22

219

Views

Are there any power identities which don't belong to this list?

Published on 27 Mar 2026 - 15:19

score 201 · Answer 12 · 2019-04-06 05:53:38

201

Views

Prove that $x^n=\sum_{k=1}^{n}\sum_{j=1}^{k}(-1)^{k-j}\binom{k}{j}\binom{x}{k}j^n$

Published on 06 Apr 2019 - 5:53

score 224 · Answer 13 · 2019-04-06 15:14:25

224

Views

Simplify the sum $ \sum_{i=0}^{k}(-1)^i i \binom{n}{i} \binom{n}{k-i}$

Published on 06 Apr 2019 - 15:14

score 323 · Answer 14 · 2026-03-27 16:53:50

323

Views

Efficient and accurate approximatiion of logarithm of binomial coefficients

Published on 27 Mar 2026 - 16:53

score 178 · Answer 15 · 2026-03-26 12:50:11

178

Views

How can I find the sum of squares of binomial coefficient and fibonacci numbers $ \sum_{k=0}^{n} \left[ \binom{n}{k}F_k \right]^2 $

Published on 26 Mar 2026 - 12:50

List Question

How do you prove that $\binom{n}{d} = \Theta(n^d)$?

Some clarifications about Pascal's rule needed.

General Leibniz's rule, why cases k=0 and k=n are separated from the sum?

$ {q \choose m} = 0$, for all $m = 1, ..., q-1$.

Verify the coefficient of $x^n$ from expansion is $\binom{2n+1}{n}$

Distribute m=17 cards to n=7 entities

Pascal triangle with more numbers to add

Calculate $\sum_{0 \le k } \binom{n+k}{2k} \binom{2k}{k} \frac{(-1)^k}{k+1}$

Find the coefficient of a term in the expansion of an algebraic expression

If $C_0, C_1, C_2, .., C_n$ are the binomial coefficients in the expansion of $(1+x)^n$

Are there any power identities which don't belong to this list?

Prove that $x^n=\sum_{k=1}^{n}\sum_{j=1}^{k}(-1)^{k-j}\binom{k}{j}\binom{x}{k}j^n$

Simplify the sum $ \sum_{i=0}^{k}(-1)^i i \binom{n}{i} \binom{n}{k-i}$

Efficient and accurate approximatiion of logarithm of binomial coefficients

How can I find the sum of squares of binomial coefficient and fibonacci numbers $ \sum_{k=0}^{n} \left[ \binom{n}{k}F_k \right]^2 $

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