Question

Hermite's identity for sum of floor function

score 351 · Answer 1 · 2026-04-02 00:59:39

351

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Hermite's identity for sum of floor function

Published on 02 Apr 2026 - 0:59

score 4.4k · Answer 2 · 2016-02-25 20:43:14

4.4k

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Solve $a_n=2 a_{n-1} - a_{n-2} + 2^n$ using generating function

Published on 25 Feb 2016 - 20:43

score 139 · Answer 3 · 2016-02-26 16:43:39

139

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Find a generating function with Fibonacci

Published on 26 Feb 2016 - 16:43

score 230 · Answer 4 · 2016-02-27 20:05:50

230

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Calculate coefficients of power series

Published on 27 Feb 2016 - 20:05

score 107 · Answer 5 · 2016-02-28 15:49:09

107

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Calculate $a_n = \binom{n}{2} + \binom{2}{n}$

Published on 28 Feb 2016 - 15:49

score 40 · Answer 6 · 2016-02-29 05:22:16

40

Views

When can a function be represented by an infinite nested radical, a la a Taylor series?

Published on 29 Feb 2016 - 5:22

score 233 · Answer 7 · 2026-03-31 16:27:34

233

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How to simplify this equation regarding pronic numbers for integer solutions

Published on 31 Mar 2026 - 16:27

score 267 · Answer 8 · 2016-03-01 14:29:28

267

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Probability Generating Function homework question

Published on 01 Mar 2016 - 14:29

score 509 · Answer 9 · 2026-03-29 02:36:06

509

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Does the functional equation $p(x^2)=p(x)p(x+1)$ have a combinatorial interpretation?

Published on 29 Mar 2026 - 2:36

score 125 · Answer 10 · 2026-04-01 00:21:06

125

Views

Help with finding the generating function of this language?

Published on 01 Apr 2026 - 0:21

score 917 · Answer 11 · 2026-04-05 17:20:57

917

Views

Formula for a geometric series weighted by binomial coefficients (sum over the upper index):$\sum_{i=0}^L {n+i\choose n}\ x^i =\ ?$

Published on 05 Apr 2026 - 17:20

score 652 · Answer 12 · 2026-04-01 00:28:28

652

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Words built from $\{0,1,2\}$ with restrictions which are not so easy to accomodate.

Published on 01 Apr 2026 - 0:28

score 1.3k · Answer 13 · 2026-04-02 00:58:23

1.3k

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Function that produces sequence 112123123412345...

Published on 02 Apr 2026 - 0:58

score 61 · Answer 14 · 2016-03-07 18:35:18

61

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How does $\frac4{1-x^3}=\sum_{n\ge 0}4x^{3n}$ equal $4x^0+0x^1+0x^2+4x^3+0x^4+0x^5+4x^6+0x^7+0x^8+\ldots$?

Published on 07 Mar 2016 - 18:35

score 36 · Answer 15 · 2016-03-08 01:13:44

36

Views

Is $\sum_{n,m \geq 0} F_n^m x^n y^m$ a rational generating function?

Published on 08 Mar 2016 - 1:13

List Question

Hermite's identity for sum of floor function

Solve $a_n=2 a_{n-1} - a_{n-2} + 2^n$ using generating function

Find a generating function with Fibonacci

Calculate coefficients of power series

Calculate $a_n = \binom{n}{2} + \binom{2}{n}$

When can a function be represented by an infinite nested radical, a la a Taylor series?

How to simplify this equation regarding pronic numbers for integer solutions

Probability Generating Function homework question

Does the functional equation $p(x^2)=p(x)p(x+1)$ have a combinatorial interpretation?

Help with finding the generating function of this language?

Formula for a geometric series weighted by binomial coefficients (sum over the upper index):$\sum_{i=0}^L {n+i\choose n}\ x^i =\ ?$

Words built from $\{0,1,2\}$ with restrictions which are not so easy to accomodate.

Function that produces sequence 112123123412345...

How does $\frac4{1-x^3}=\sum_{n\ge 0}4x^{3n}$ equal $4x^0+0x^1+0x^2+4x^3+0x^4+0x^5+4x^6+0x^7+0x^8+\ldots$?

Is $\sum_{n,m \geq 0} F_n^m x^n y^m$ a rational generating function?

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