Question

How to solve recurrence relations using generating functions that do not start at $a_0$?

score 387 · Answer 1 · 2026-04-11 14:28:04

387

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How to solve recurrence relations using generating functions that do not start at $a_0$?

Published on 11 Apr 2026 - 14:28

score 456 · Answer 2 · 2017-11-09 00:20:29

456

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How can I find the coefficient of $x^{23}$ in $(x^3+x^4+x^5+x^6)^4$?

Published on 09 Nov 2017 - 0:20

score 117 · Answer 3 · 2017-11-09 22:11:46

117

Views

Using EGFs to solve the recurrence relation $a_n=n a_{n-1}+(n+1)!$

Published on 09 Nov 2017 - 22:11

score 239 · Answer 4 · 2026-04-11 08:00:09

239

Views

Creating Generating Function

Published on 11 Apr 2026 - 8:00

score 158 · Answer 5 · 2017-11-11 23:10:48

158

Views

Given the sequence {39, 174, 441, 876, 1515, ....}, find the generating function

Published on 11 Nov 2017 - 23:10

score 89 · Answer 6 · 2026-04-12 03:58:07

89

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Partition Generating Functions

Published on 12 Apr 2026 - 3:58

score 1.6k · Answer 7 · 2026-04-12 11:45:46

1.6k

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Algorithm for computing Hadamard product of two rational generating functions

Published on 12 Apr 2026 - 11:45

score 45 · Answer 8 · 2026-04-09 16:43:30

45

Views

Combinatorial generating function networks

Published on 09 Apr 2026 - 16:43

score 645 · Answer 9 · 2017-11-15 23:32:18

645

Views

Producing Exponential Generating Functions For Coefficients

Published on 15 Nov 2017 - 23:32

score 58 · Answer 10 · 2017-11-16 20:30:56

58

Views

Number of solutions to $a + b + c + d + f = n$ in nonnegative integers $a, b, c, d, f,$ given restrictions on $a, b,$ and $f$

Published on 16 Nov 2017 - 20:30

score 457 · Answer 11 · 2026-04-09 08:37:17

457

Views

How to get the explicit formula of Bernoulli polynomial using its generating function?

Published on 09 Apr 2026 - 8:37

score 362 · Answer 12 · 2026-04-12 15:26:26

362

Views

Harmonic number identity $\sum_{k=1}^{n}H_k=(n+1)(H_{n+1}-1)$

Published on 12 Apr 2026 - 15:26

score 322 · Answer 13 · 2017-11-19 03:53:45

322

Views

Ordinary Generating Function for the number of solution :$ x_1 + x_2 + \cdot\cdot\cdot + x_k = n$

Published on 19 Nov 2017 - 3:53

score 83 · Answer 14 · 2026-04-09 11:38:44

83

Views

How do we convert a generating function that counts to a generating function of probabilities?

Published on 09 Apr 2026 - 11:38

score 186 · Answer 15 · 2026-04-13 09:51:14

186

Views

Finding the closed form of two intertwined recurrence relations

Published on 13 Apr 2026 - 9:51

List Question

How to solve recurrence relations using generating functions that do not start at $a_0$?

How can I find the coefficient of $x^{23}$ in $(x^3+x^4+x^5+x^6)^4$?

Using EGFs to solve the recurrence relation $a_n=n a_{n-1}+(n+1)!$

Creating Generating Function

Given the sequence {39, 174, 441, 876, 1515, ....}, find the generating function

Partition Generating Functions

Algorithm for computing Hadamard product of two rational generating functions

Combinatorial generating function networks

Producing Exponential Generating Functions For Coefficients

Number of solutions to $a + b + c + d + f = n$ in nonnegative integers $a, b, c, d, f,$ given restrictions on $a, b,$ and $f$

How to get the explicit formula of Bernoulli polynomial using its generating function?

Harmonic number identity $\sum_{k=1}^{n}H_k=(n+1)(H_{n+1}-1)$

Ordinary Generating Function for the number of solution :$ x_1 + x_2 + \cdot\cdot\cdot + x_k = n$

How do we convert a generating function that counts to a generating function of probabilities?

Finding the closed form of two intertwined recurrence relations

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