Question

Proof using Generating Functions

score 231 · Answer 1 · 2019-11-17 12:16:20

231

Views

Proof using Generating Functions

Published on 17 Nov 2019 - 12:16

score 153 · Answer 2 · 2026-03-27 06:59:51

153

Views

Using generating functions to find the number of compositions

Published on 27 Mar 2026 - 6:59

score 70 · Answer 3 · 2026-03-25 13:54:44

70

Views

Understanding derivation of Catalan Numbers

Published on 25 Mar 2026 - 13:54

score 56 · Answer 4 · 2019-11-18 15:29:48

56

Views

Compute - Coefficient Extraction

Published on 18 Nov 2019 - 15:29

score 68 · Answer 5 · 2026-03-26 03:05:56

68

Views

Finding a generating function for a formal power series containing $n$ and $a_n$

Published on 26 Mar 2026 - 3:05

score 243 · Answer 6 · 2026-03-26 12:51:32

243

Views

finite sum with combinatorics

Published on 26 Mar 2026 - 12:51

score 904 · Answer 7 · 2019-11-19 17:38:38

904

Views

In how many ways can we select $r$ balls from a set consisting of $3$ red, $3$ yellow, $3 $ black and $3$ blue balls?

Published on 19 Nov 2019 - 17:38

score 318 · Answer 8 · 2019-11-19 19:58:08

318

Views

Let $(a_n)$ denote the number of ways to place parenthesis to multiply $n$ numbers $k_1,k_2\ldots k_n$. Find a recurrence relation for $ (a_n)$

Published on 19 Nov 2019 - 19:58

score 47 · Answer 9 · 2019-11-19 23:19:01

47

Views

Solve the recurrence $a_n=a_{n-1} + 6a_{n-2} + 5\cdot3^n\; \forall n\geq 2\;\;a_0=4\;\; a_1=6$

Published on 19 Nov 2019 - 23:19

score 509 · Answer 10 · 2026-03-27 06:05:27

509

Views

Distributing identical objects into identical boxes using generating functions

Published on 27 Mar 2026 - 6:05

score 366 · Answer 11 · 2026-03-27 06:05:30

366

Views

Partition function and "Euler function" - what does it mean?

Published on 27 Mar 2026 - 6:05

score 76 · Answer 12 · 2019-11-20 17:32:49

76

Views

Generating function of $\sum_{i=1}^8 a_i=n$ with $\sum_{i=1}^4 a_i$ even and $\sum_{i=5}^8 a_i$ odd

Published on 20 Nov 2019 - 17:32

score 54 · Answer 13 · 2026-03-26 12:53:30

54

Views

Is there a combinatorial proof of the Taylor series $\frac1{\sqrt{1-4x}}=\sum_{n=0}^\infty{2n\choose n}x^n$?

Published on 26 Mar 2026 - 12:53

score 184 · Answer 14 · 2019-11-22 01:05:28

184

Views

Help with an exponential/generating functions problem.

Published on 22 Nov 2019 - 1:05

score 109 · Answer 15 · 2019-11-22 17:10:34

109

Views

generating function for distribution of 12 balls into 10 cells

Published on 22 Nov 2019 - 17:10

List Question

Proof using Generating Functions

Using generating functions to find the number of compositions

Understanding derivation of Catalan Numbers

Compute - Coefficient Extraction

Finding a generating function for a formal power series containing $n$ and $a_n$

finite sum with combinatorics

In how many ways can we select $r$ balls from a set consisting of $3$ red, $3$ yellow, $3 $ black and $3$ blue balls?

Let $(a_n)$ denote the number of ways to place parenthesis to multiply $n$ numbers $k_1,k_2\ldots k_n$. Find a recurrence relation for $ (a_n)$

Solve the recurrence $a_n=a_{n-1} + 6a_{n-2} + 5\cdot3^n\; \forall n\geq 2\;\;a_0=4\;\; a_1=6$

Distributing identical objects into identical boxes using generating functions

Partition function and "Euler function" - what does it mean?

Generating function of $\sum_{i=1}^8 a_i=n$ with $\sum_{i=1}^4 a_i$ even and $\sum_{i=5}^8 a_i$ odd

Is there a combinatorial proof of the Taylor series $\frac1{\sqrt{1-4x}}=\sum_{n=0}^\infty{2n\choose n}x^n$?

Help with an exponential/generating functions problem.

generating function for distribution of 12 balls into 10 cells

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