Some Binomial Coefficient Identities of Specific and General Type - Larsen, Mogens E.; Larcombe, Peter J. (Utilitas Mathematica, 2007)
Underpinned by the falling factorial function, we first give proofs of three specific binomial coefficient identities involving Harmonic numbers which are special cases of a 1996 result due to Kirschenhofer. Using this same tool we then go on to develop some other related identities. In particular, two of them lead to a generalised formula - dealing with binomial coefficient sums of certain type - which is believed by the authors to be a new one.