List questions from generating-functions

Published on 13 Apr 2026 - 18:30

165

Views

Finding a closed-form formula to a recurrence with summation of past terms

Published on 09 Apr 2026 - 15:24

461

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Find the coefficient of $x^n$ in $(x^2 +x^3 +x^4 +\cdots)^5$

Published on 16 Apr 2026 - 19:10

192

Views

Solve generating function for $a_n$

Published on 13 Apr 2026 - 23:56

92

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Alternating sum of binomials divided by a polynomial of the index

Published on 13 Apr 2026 - 21:19

70

Views

Consider $5$ dice with six sides, three of which are labeled $1$ and three of which are labeled $2$. How many ways are there to get a sum of $9$?

Published on 15 Apr 2026 - 8:35

117

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Solving recursive equation with convoluted recursion (with application to backward error analysis of ODE)

Published on 09 Apr 2026 - 23:49

165

Views

Find the general term in the sequence with generating function

Published on 13 Apr 2026 - 7:12

139

Views

Binomial Coefficient

Published on 14 Apr 2026 - 9:29

76

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How do I use generating functions?

Published on 09 Apr 2026 - 9:38

51

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How to find $\sum_{n=1}^{\infty} a_{2n} x^n$ from $\sum_{n=1}^{\infty} a_{n}x^n$?

Published on 14 Apr 2026 - 12:45

87

Views

Demonstration for the equal number of odd and unequal partitions of an integer

Published on 16 Apr 2026 - 15:24

73

Views

Show that $\sum_{k=1}^n \binom{n}{k}k^2=n^2\cdot \:2^{n-2}+n\cdot \:2^{n-2}$.

Published on 17 Apr 2026 - 14:48

148

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Understaing Concept of Generating function.

Published on 11 Apr 2026 - 7:53

90

Views

How to solve $x(x-1)(x-2)(x-3)(x-4)(x-5)....(x-999)$?

Published on 17 Apr 2026 - 9:18

List Question

Recurrence relations in the generating function of binary partitions

Finding a closed-form formula to a recurrence with summation of past terms

Find the coefficient of $x^n$ in $(x^2 +x^3 +x^4 +\cdots)^5$

Solve generating function for $a_n$

Alternating sum of binomials divided by a polynomial of the index

Consider $5$ dice with six sides, three of which are labeled $1$ and three of which are labeled $2$. How many ways are there to get a sum of $9$?

Solving recursive equation with convoluted recursion (with application to backward error analysis of ODE)

Find the general term in the sequence with generating function

Binomial Coefficient

How do I use generating functions?

How to find $\sum_{n=1}^{\infty} a_{2n} x^n$ from $\sum_{n=1}^{\infty} a_{n}x^n$?

Demonstration for the equal number of odd and unequal partitions of an integer

Show that $\sum_{k=1}^n \binom{n}{k}k^2=n^2\cdot \:2^{n-2}+n\cdot \:2^{n-2}$.

Understaing Concept of Generating function.

How to solve $x(x-1)(x-2)(x-3)(x-4)(x-5)....(x-999)$?

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