Question

Simplifying $\sum_{r = 0}^{n} {{n}\choose{r}}r^k(-1)^r$

score 344 · Answer 1 · 2016-07-30 05:43:16

344

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Simplifying $\sum_{r = 0}^{n} {{n}\choose{r}}r^k(-1)^r$

Published on 30 Jul 2016 - 5:43

score 116 · Answer 2 · 2016-07-30 06:14:43

116

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A Problem with the Generating Function of Fibonacci.

Published on 30 Jul 2016 - 6:14

score 66 · Answer 3 · 2026-03-30 17:04:18

66

Views

Is my use of derivatives correct in this infinite sum?

Published on 30 Mar 2026 - 17:04

score 80 · Answer 4 · 2016-08-01 14:11:48

80

Views

Find sum of expressions $x_1\dotsb x_k$ where summation is over solutions for $n=x_1+\dots+x_k$

Published on 01 Aug 2016 - 14:11

score 80 · Answer 5 · 2016-08-01 20:38:59

80

Views

distribute 25 objects into 7 bins with constraints using generating functions

Published on 01 Aug 2016 - 20:38

score 169 · Answer 6 · 2016-08-02 20:08:29

169

Views

Using generating functions to solve a recurrence

Published on 02 Aug 2016 - 20:08

score 251 · Answer 7 · 2026-03-28 18:12:58

251

Views

Hypergeometric function generating function

Published on 28 Mar 2026 - 18:12

score 182 · Answer 8 · 2026-03-27 01:13:30

182

Views

Closed form for probabilities from generating function of queue length in M/D/1 queue.

Published on 27 Mar 2026 - 1:13

score 180 · Answer 9 · 2026-03-29 05:35:15

180

Views

generating function: how many possibilities are there to throw 10 different dice so that their sum is 25

Published on 29 Mar 2026 - 5:35

score 129 · Answer 10 · 2016-08-05 17:53:57

129

Views

how to prove this by using generating functions coefficient?

Published on 05 Aug 2016 - 17:53

score 409 · Answer 11 · 2016-08-06 18:41:09

409

Views

Challenging recurrence relation that depends on composition of integers

Published on 06 Aug 2016 - 18:41

score 395 · Answer 12 · 2026-03-30 21:15:45

395

Views

Can double generating functions be used to solve this?

Published on 30 Mar 2026 - 21:15

score 1.4k · Answer 13 · 2016-08-07 20:40:59

1.4k

Views

Find the coefficient of $x^n$ in generating function $\frac{1}{(1-x)^3(1+x)}$

Published on 07 Aug 2016 - 20:40

score 1.2k · Answer 14 · 2016-08-08 04:15:16

1.2k

Views

Important identities that can be obtained by manipulating the function $\frac{x}{e^x-1} = \frac{B_0}{0!} + \frac{B_1}{1!}x + \frac{B_2}{2!}x^2 + ...$?

Published on 08 Aug 2016 - 4:15

score 85 · Answer 15 · 2016-08-08 08:07:08

85

Views

Proving generating functions equality.

Published on 08 Aug 2016 - 8:07

List Question

Simplifying $\sum_{r = 0}^{n} {{n}\choose{r}}r^k(-1)^r$

A Problem with the Generating Function of Fibonacci.

Is my use of derivatives correct in this infinite sum?

Find sum of expressions $x_1\dotsb x_k$ where summation is over solutions for $n=x_1+\dots+x_k$

distribute 25 objects into 7 bins with constraints using generating functions

Using generating functions to solve a recurrence

Hypergeometric function generating function

Closed form for probabilities from generating function of queue length in M/D/1 queue.

generating function: how many possibilities are there to throw 10 different dice so that their sum is 25

how to prove this by using generating functions coefficient?

Challenging recurrence relation that depends on composition of integers

Can double generating functions be used to solve this?

Find the coefficient of $x^n$ in generating function $\frac{1}{(1-x)^3(1+x)}$

Important identities that can be obtained by manipulating the function $\frac{x}{e^x-1} = \frac{B_0}{0!} + \frac{B_1}{1!}x + \frac{B_2}{2!}x^2 + ...$?

Proving generating functions equality.

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