
Archives
 May 2020
 March 2020
 February 2020
 January 2020
 December 2019
 September 2019
 August 2019
 July 2019
 June 2019
 May 2019
 April 2019
 March 2019
 February 2019
 January 2019
 December 2018
 November 2018
 October 2018
 September 2018
 August 2018
 July 2018
 June 2018
 May 2018
 April 2018
 March 2018
 February 2018
 January 2018
 December 2017
 November 2017
 October 2017
 September 2017
 August 2017
 July 2017
 June 2017
 May 2017
 April 2017
 March 2017
 February 2017
 January 2017
 December 2016
 November 2016
 October 2016
 September 2016
 August 2016
 July 2016
 June 2016
 May 2016
 April 2016
 March 2016
 February 2016
 January 2016
 December 2015
 November 2015
 October 2015
 September 2015
 August 2015
 July 2015
 June 2015
 May 2015
 April 2015
 March 2015
 February 2015
 January 2015
 December 2014
 November 2014
 October 2014
 September 2014
 August 2014
 July 2014
 June 2014
 May 2014
 April 2014
 March 2014
 February 2014
 January 2014
 December 2013
 November 2013
 October 2013
 September 2013
 June 2013
 May 2013
 April 2013
 March 2013
 February 2013
 January 2013
 December 2012
 November 2012
 October 2012
 September 2012
 August 2012
 July 2012
 May 2012
 March 2012
 February 2012
 January 2012
 December 2011
 November 2011
 October 2011

Meta
Category Archives: Stirling numbers
A Proof of Dobinski’s Formula for Bell Numbers
Dobinski’s formula entails the following infinite series expression for the nth Bell number : In this post we’ll work through a proof of Dobinski’s formula. We’ll need four formulas: The Maclaurin series for : . The formula for converting normal powers to falling … Continue reading
Posted in Bell numbers, sequences and series, Stirling numbers
2 Comments
Combinatorial Proofs for the Binomial and Alternating Binomial Power Sums
In this post I give combinatorial proofs of formulas for the binomial and alternating binomial power sums: and Here’s the first. Identity 1. . Proof. Both sides count the number of functions from to subsets of . For the left … Continue reading
Posted in binomial coefficients, combinatorics, Stirling numbers
1 Comment
A Combinatorial Proof for the Power Sum
Probably the most common formula for the power sum is the one involving binomial coefficients and Bernoulli numbers , sometimes called Faulhaber’s formula: Historically, this, or a variant of it, was the first general formula for the power sum. There … Continue reading
A Combinatorial Proof of a Stirling Number Formula
One of the fundamental properties of the (unsigned) Stirling numbers of the first kind is that they can be used to convert from rising factorial powers to ordinary powers via the formula This post gives a combinatorial proof of this … Continue reading
Posted in combinatorics, Stirling numbers
Leave a comment