Discrete MathematicsVolume 205, Issues 1–3, 28 July 1999, Pages 207-210NoteA Characterization of the bell numbersAuthor links open overlay panelMartin AignerShow moreShareCitehttps://doi.org/10.1016/S0012-365X(99)00108-9Get rights and contentUnder an Elsevier user licenseopen archiveAbstractLet Bn be the Bell numbers, and Ãn(n⩾0), B̃n(n⩾1) be the matrices defined by Ãn(i,j)=Bi+j(0⩽i,j⩽n),B̃n(i,j)=Bi+j+1(0⩽i,j⩽n). It is shown that (Bn) is the unique sequence of real numbers such that detÃn=detB̃n=n!! for all n, where n!!=∏k=0n(k!).Previous article in issueNext article in issueRecommended articlesCited by (0)Copyright © 1999 Elsevier Science B.V. All rights reserved.