User Ira Gessel

13 votes

Combinatorial identities

answered Nov 27, 2013 at 16:48

12 votes

Exponential of a specific hypergeometric series

answered Feb 5, 2014 at 14:38

12 votes

Interpolating a sum of binomial coefficients using a sin function

answered Oct 11, 2012 at 18:06

12 votes

The proportion between permutations and derangements.

answered Jun 16, 2013 at 19:58

12 votes

Accepted

"MultiCatalan numbers"

answered Oct 14, 2013 at 17:58

12 votes

A recurrence relation on Catalan numbers

answered Dec 26, 2014 at 21:54

12 votes

Accepted

A combinatorial identity involving harmonic numbers

answered Jun 1, 2017 at 14:13

12 votes

A combinatorial identity

answered Aug 14, 2017 at 2:50

12 votes

Series involving power of the index

answered May 29, 2022 at 1:55

12 votes

Accepted

Help finding an analytic continuation

answered Jun 27, 2023 at 20:39

12 votes

Accepted

A combinatorial interpretation for $n$-ary trees for negative $n$

answered Mar 4, 2023 at 6:24

11 votes

Positivity of a one-variable rational function

answered Mar 31, 2022 at 16:17

11 votes

Accepted

Reference request: Gessel interview's generating function identities

answered May 13 at 16:27

10 votes

Accepted

Diagonal analogue of symmetric functions

answered Nov 30 at 5:43

10 votes

Accepted

Generating function for "descents" and "cycle-types", in tandem

answered Apr 8, 2022 at 0:50

10 votes

Asking for a proof for a sum of products of binomials: an "interesting" identity?

answered Jan 12, 2022 at 20:30

10 votes

Accepted

Double q-analog of Pochhammer

answered Nov 15, 2023 at 15:29

10 votes

Accepted

Identity with Pochhammer and harmonic numbers

answered May 31, 2017 at 5:58

10 votes

Prominent non-mathematical work of mathematicians

answered Jul 22, 2021 at 4:43

10 votes

Accepted

Congruence for complementary Bell numbers

answered Dec 14, 2016 at 16:59

10 votes

Accepted

Sum of products of exponentials and polynomials

answered Nov 22, 2011 at 16:02

10 votes

Counting card distributions when cards are duplicated

answered Feb 18, 2011 at 17:40

10 votes

Faà di Bruno's formula for inverse functions?

answered May 31, 2012 at 20:15

9 votes

Identity for Power Series and Binomial Coefficients

answered Jan 26, 2015 at 22:22

9 votes

Combinatorial counting with symmetry

answered May 18, 2014 at 16:11

9 votes

Method to evaluate an infinite sum of ratio of Gamma functions (how does Mathematica do it?)

answered Feb 19, 2021 at 17:20

9 votes

Accepted

Explicit formula for a generating function

answered Jun 16, 2018 at 14:36

9 votes

Accepted

A sequence of polynomials related to Catalan numbers

answered Nov 4, 2022 at 20:26

8 votes

Accepted

Infinite sum of Laguerre polynomials: is $\sum_{k=0}^{\infty}\frac{n!}{(k+n)!}x^kL_n^k(x)^2=e^x+P(x)$, with $P$ a polynomial of degree $2n-1$?

answered Mar 12, 2022 at 4:12

8 votes

Accepted

Finite sum with falling factorial

answered Mar 25, 2021 at 20:31

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191 Answers

Combinatorial identities

Exponential of a specific hypergeometric series

Interpolating a sum of binomial coefficients using a sin function

The proportion between permutations and derangements.

"MultiCatalan numbers"

A recurrence relation on Catalan numbers

A combinatorial identity involving harmonic numbers

A combinatorial identity

Series involving power of the index

Help finding an analytic continuation

A combinatorial interpretation for $n$-ary trees for negative $n$

Positivity of a one-variable rational function

Reference request: Gessel interview's generating function identities

Diagonal analogue of symmetric functions

Generating function for "descents" and "cycle-types", in tandem

Asking for a proof for a sum of products of binomials: an "interesting" identity?

Double q-analog of Pochhammer

Identity with Pochhammer and harmonic numbers

Prominent non-mathematical work of mathematicians

Congruence for complementary Bell numbers

Sum of products of exponentials and polynomials

Counting card distributions when cards are duplicated

Faà di Bruno's formula for inverse functions?

Identity for Power Series and Binomial Coefficients

Combinatorial counting with symmetry

Method to evaluate an infinite sum of ratio of Gamma functions (how does Mathematica do it?)

Explicit formula for a generating function

A sequence of polynomials related to Catalan numbers

Infinite sum of Laguerre polynomials: is $\sum_{k=0}^{\infty}\frac{n!}{(k+n)!}x^kL_n^k(x)^2=e^x+P(x)$, with $P$ a polynomial of degree $2n-1$?

Finite sum with falling factorial