New posts in generating-functions

Closed formula for the sums $\sum\limits_{1 \le i_1 < i_2 < \dots < i_k \le n} i_1 i_2 \cdots i_k $?

combinatorics summation generating-functions closed-form

Generating functions - deriving a formula for the sum $1^2 + 2^2 +\cdots+n^2$

discrete-mathematics generating-functions

Finding coefficient of generating function

combinatorics generating-functions

Toward Explicit Formula from Recursion : Is Generating function "the only" answer?

combinatorics recurrence-relations generating-functions recursion

Flipping a set of unfair coins [closed]

probability statistics generating-functions

Recurrence relations in the generating function of binary partitions

generating-functions binary integer-partitions

swap $\sum_k^\infty\sum_j^k$ [duplicate]

summation generating-functions

Counting sets by their connectedness

combinatorics discrete-mathematics graph-theory computer-science generating-functions

Looking for a closed form solution $P_{n+2}(x)=x^2 P'_{n+1}(x)+(n+1)xP_{n+1}(x)-(n+1)P'_n(x) $

derivatives polynomials partial-differential-equations recurrence-relations generating-functions

What is the meaning of the cumulant generating function itself?

probability-theory generating-functions moment-generating-functions

Towards a Little proof of Fermat's last theorem

real-analysis number-theory diophantine-equations generating-functions

Composition of Formal Power Series is associative

generating-functions

Analyzing the Coefficient of a generating function and its asymptotic

combinatorics asymptotics generating-functions

Recurrences for even and odd indexed of Fibonacci Numbers

combinatorics discrete-mathematics generating-functions fibonacci-numbers

How to fit $\sum{n^{2}x^{n}}$ into a generating function?

sequences-and-series generating-functions

Generating function for gamma function (or factorial)

combinatorics generating-functions factorial gamma-function

Is there a recursive formula for Euler's Totient function

generating-functions recursion totient-function multiplicative-function

How to solve second degree recurrence relation?

combinatorics recurrence-relations generating-functions summation

In generatingfunctionology, for a polynomial $P$ and a differential operator $D$, what does $P(xD)$ mean?

notation generating-functions

Is there any closed form for the following series?

generating-functions closed-form