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A Characterization of the bell numbers

https://doi.org/10.1016/S0012-365X(99)00108-9Get rights and content
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Abstract

Let 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!).

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