New posts in generating-functions

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

discrete-mathematics generating-functions

The number of ways to write a positive integer as the sum of distinct parts with a fixed length

combinatorics number-theory generating-functions integer-partitions

Coefficient extraction

calculus algorithms binomial-coefficients generating-functions harmonic-numbers

Does the functional equation $p(x^2)=p(x)p(x+1)$ have a combinatorial interpretation?

combinatorics polynomials generating-functions alternative-proof combinatorial-proofs

Closed form of a generating function $\sum _{n=1}^\infty x^{n^2}$

combinatorics number-theory generating-functions closed-form

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 $9$?

combinatorics generating-functions

Dealing with a difficult sum of binomial coefficients, $\sum_{l=0}^{n}\binom{n}{l}^{2}\sum_{j=0}^{2l-n}\binom{l}{j} $

combinatorics summation asymptotics binomial-coefficients generating-functions

How can i find closed-form expression of generating function of this series? [closed]

combinatorics generating-functions

Making an infinite generating function a finite one

number-theory recurrence-relations generating-functions

Find the general term in the sequence with generating function

sequences-and-series generating-functions

Generating function for the solutions of equation $ 2x_1 + 4x_2 = n$

combinatorics generating-functions

Proving that odd partitions and distinct partitions are equal

sequences-and-series generating-functions infinite-product integer-partitions q-series

Infinite geometric sum (asking for insight on an easier solution)

sequences-and-series summation contest-math generating-functions

Asymptotics of a recursive sequence

real-analysis combinatorics complex-analysis asymptotics generating-functions

Finding a combinatorial formula for the following sequence of tables

combinatorics generating-functions puzzle pattern-recognition

Challenging identity regarding Bell polynomials

combinatorics summation generating-functions closed-form stirling-numbers

Generating functions for context-free languages

combinatorics generating-functions formal-languages context-free-grammar

Deep understanding on exponential generating function

combinatorics generating-functions

Generalizing Ramanujan's sum of cubes identity?

sequences-and-series elementary-number-theory generating-functions

Prove that $\exp(\log(\frac{1}{1-x})) = \frac{1}{1-x}$

combinatorics binomial-coefficients power-series generating-functions