Question

Closed form for a formula with a summation over $i\binom{n-i}{k-1}$, and combinatorial proof?

score 346 · Answer 1 · 2026-04-15 06:30:15

346

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Closed form for a formula with a summation over $i\binom{n-i}{k-1}$, and combinatorial proof?

Published on 15 Apr 2026 - 6:30

score 220 · Answer 2 · 2026-04-15 19:46:47

220

Views

Sum concerning Catalan triangle and binomials

Published on 15 Apr 2026 - 19:46

score 135 · Answer 3 · 2026-04-15 21:59:21

135

Views

prove by inductive step

Published on 15 Apr 2026 - 21:59

score 165 · Answer 4 · 2026-04-11 01:21:10

165

Views

An inequality concerning non-negative integer matrices with constant row and column sums

Published on 11 Apr 2026 - 1:21

score 2.6k · Answer 5 · 2026-04-14 09:29:13

2.6k

Views

Binomial coefficients identity: $\sum i \binom{n-i}{k-1}=\binom{n+1}{k+1}$

Published on 14 Apr 2026 - 9:29

score 298 · Answer 6 · 2026-04-09 11:08:07

298

Views

Need help finding a closed form for complicated sum

Published on 09 Apr 2026 - 11:08

score 301 · Answer 7 · 2026-04-11 09:45:04

301

Views

Sum problem involving Factorials

Published on 11 Apr 2026 - 9:45

score 3.7k · Answer 8 · 2026-04-15 12:26:54

3.7k

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$\sum_{k=0}^n (-1)^k \binom{n}{k}^2$ and $\sum_{k=0}^n k \binom{n}{k}^2$

Published on 15 Apr 2026 - 12:26

score 222 · Answer 9 · 2026-04-16 09:47:16

222

Views

A combinatorial identity: $\sum _{i + j = k} (-1)^i {n \choose i} {n + j - 1 \choose n - 1 } = 0 $

Published on 16 Apr 2026 - 9:47

score 108 · Answer 10 · 2026-04-15 07:40:38

108

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Find the value of $ \sum _{r=0} ^{2n} r ( ^{2n}C _r) ( \frac 1{r+2} ) $

Published on 15 Apr 2026 - 7:40

score 52 · Answer 11 · 2026-04-16 16:46:07

52

Views

$X_n = \sqrt[k]{n^{p}+an^{q}+1}-\sqrt[k]{n^{p}+bn^{q}+1} $

Published on 16 Apr 2026 - 16:46

score 209 · Answer 12 · 2026-04-16 00:12:30

209

Views

How to find $ \binom {1}{k} + \binom {2}{k} + \binom{3}{k} + ... + \binom{n}{k} $

Published on 16 Apr 2026 - 0:12

score 667 · Answer 13 · 2026-04-16 11:07:44

667

Views

Finite summation with binomial coefficients, $\sum (-1)^k\binom{r}{k} \binom{k/2}{q}$

Published on 16 Apr 2026 - 11:07

score 1.1k · Answer 14 · 2026-04-12 21:09:39

1.1k

Views

How many routes are there that pass through at most one congested intersection

Published on 12 Apr 2026 - 21:09

score 390 · Answer 15 · 2026-04-15 21:17:33

390

Views

Combinatorial proof for $ \sum _{r=1} ^n r^3 \binom nr = n^2(n+3) 2^{n-3}$

Published on 15 Apr 2026 - 21:17

List Question

Closed form for a formula with a summation over $i\binom{n-i}{k-1}$, and combinatorial proof?

Sum concerning Catalan triangle and binomials

prove by inductive step

An inequality concerning non-negative integer matrices with constant row and column sums

Binomial coefficients identity: $\sum i \binom{n-i}{k-1}=\binom{n+1}{k+1}$

Need help finding a closed form for complicated sum

Sum problem involving Factorials

$\sum_{k=0}^n (-1)^k \binom{n}{k}^2$ and $\sum_{k=0}^n k \binom{n}{k}^2$

A combinatorial identity: $\sum _{i + j = k} (-1)^i {n \choose i} {n + j - 1 \choose n - 1 } = 0 $

Find the value of $ \sum _{r=0} ^{2n} r ( ^{2n}C _r) ( \frac 1{r+2} ) $

$X_n = \sqrt[k]{n^{p}+an^{q}+1}-\sqrt[k]{n^{p}+bn^{q}+1} $

How to find $ \binom {1}{k} + \binom {2}{k} + \binom{3}{k} + ... + \binom{n}{k} $

Finite summation with binomial coefficients, $\sum (-1)^k\binom{r}{k} \binom{k/2}{q}$

How many routes are there that pass through at most one congested intersection

Combinatorial proof for $ \sum _{r=1} ^n r^3 \binom nr = n^2(n+3) 2^{n-3}$

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