New posts in generating-functions

A sequence of coefficients of $x+(x+(x+(x+(x+(x+\dots)^6)^5)^4)^3)^2$

combinatorics generating-functions integers formal-power-series oeis

Why are Stirling numbers of the first kind related to the number of permutations with $k$ cycles?

combinatorics permutations generating-functions stirling-numbers permutation-cycles

Counting integer partitions of n into exactly k distinct parts size at most M

combinatorics generating-functions integer-partitions

Unexpected Proofs Using Generating Functions

combinatorics analysis generating-functions big-list

Why do engineers use the Z-transform and mathematicians use generating functions?

sequences-and-series generating-functions integral-transforms

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

sequences-and-series combinatorics limits recurrence-relations generating-functions

Proving a binomial sum identity $\sum _{k=0}^n \binom nk \frac{(-1)^k}{2k+1} = \frac{(2n)!!}{(2n+1)!!}$

combinatorics summation binomial-coefficients generating-functions

How are we able to calculate specific numbers in the Fibonacci Sequence?

linear-algebra combinatorics generating-functions fibonacci-numbers

Combinatorial Argument for Exponential and Logarithmic Function Being Inverse

combinatorics generating-functions

A nice but somewhat challenging binomial identity

binomial-coefficients generating-functions

Expected maximum number of unpaired socks

combinatorics generating-functions

How to show that $1 \over \sqrt{1 - 4x} $ generates $\sum_{n=0}^\infty \binom{2n}{n}x^n $

sequences-and-series generating-functions

Why are generating functions useful?

combinatorics generating-functions

Find a generating function for the number of strings

combinatorics generating-functions

How many connected graphs over V vertices and E edges?

graph-theory generating-functions

Generating functions and central binomial coefficient

summation binomial-coefficients generating-functions

Factorial and exponential dual identities

analysis power-series generating-functions

Making Change for a Dollar (and other number partitioning problems)

combinatorics generating-functions integer-partitions

The generating function for the Fibonacci numbers

sequences-and-series combinatorics generating-functions fibonacci-numbers

How can I learn about generating functions?

combinatorics generating-functions