List questions from generating-functions

45

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Given $n = a_1 + \cdots+ a_k$ where $a_i$ is the number of (indistinguishable) balls with an $i$ on them.

Published on 20 Sep 2013 - 16:15

133

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Generating function of $(n+1) 2^n a_n$

Published on 23 Sep 2013 - 9:45

1.7k

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Find the generating function for the sequence ${1, 2, 1, 4, 1, 8, ...}$

Published on 25 Sep 2013 - 22:21

1.4k

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Generating function solution to previous question $a_{n}=a_{\lfloor n/2\rfloor}+a_{\lfloor n/3 \rfloor}+a_{\lfloor n/6\rfloor}$

Published on 27 Sep 2013 - 20:59

564

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Check whether $\sum\limits_{n=1}^{\infty}\frac{z^n}{(1-z^n)^k}=\sum\limits_{n=1}^{\infty}\sigma_{k-1}(n)z^n$

Published on 29 Sep 2013 - 5:42

6.8k

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About the generating function of the sum of roll dice values.

Published on 30 Sep 2013 - 17:00

1.7k

Views

CDF from generating function

Published on 10 Apr 2026 - 16:38

299

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Why do convergence issues not play a role when talking of generating functions

Published on 03 Oct 2013 - 11:16

340

Views

How to identify this power series as $k\sin(k/x)$?

Published on 07 Apr 2026 - 0:26

76

Views

Need Help with Interpreting this Answer

Published on 10 Apr 2026 - 22:20

78

Views

$k$-cubes attached to each $h$-cube in $n$-hypercube

Published on 06 Oct 2013 - 19:39

87

Views

Binomial Type sequence

Published on 10 Oct 2013 - 9:29

940

Views

Combinatorics? HELP!

Published on 11 Apr 2026 - 6:49

67

Views

multiple function recursion

Published on 09 Apr 2026 - 5:19

1.7k

Views

Generating functions word problem(balloons)

Published on 11 Apr 2026 - 13:38

List Question

Given $n = a_1 + \cdots+ a_k$ where $a_i$ is the number of (indistinguishable) balls with an $i$ on them.

Generating function of $(n+1) 2^n a_n$

Find the generating function for the sequence ${1, 2, 1, 4, 1, 8, ...}$

Generating function solution to previous question $a_{n}=a_{\lfloor n/2\rfloor}+a_{\lfloor n/3 \rfloor}+a_{\lfloor n/6\rfloor}$

Check whether $\sum\limits_{n=1}^{\infty}\frac{z^n}{(1-z^n)^k}=\sum\limits_{n=1}^{\infty}\sigma_{k-1}(n)z^n$

About the generating function of the sum of roll dice values.

CDF from generating function

Why do convergence issues not play a role when talking of generating functions

How to identify this power series as $k\sin(k/x)$?

Need Help with Interpreting this Answer

$k$-cubes attached to each $h$-cube in $n$-hypercube

Binomial Type sequence

Combinatorics? HELP!

multiple function recursion

Generating functions word problem(balloons)

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