Bernoulli Numbers and Generalized Factorial Sums

Paul Thomas Young
2011 Integers  
AbstractWe prove a pair of identities expressing Bernoulli numbers and Bernoulli numbers of the second kind as sums of generalized falling factorials. These are derived from an expression for the Mahler coefficients of degenerate Bernoulli numbers. As corollaries several unusual identities and congruences are derived.
doi:10.1515/integ.2011.041 fatcat:cpw4ktpwezdj3d2zc773hrfcuy