Two Kinds of Numbers and Their Applications

Zhi Zhang; Hong Feng
July 2006
Acta Mathematica Sinica;Jul2006, Vol. 22 Issue 4, p999
Academic Journal
C. Radoux ( J. Comput. Appl. Math. 115 (2000) 471–477) obtained a computational formula of Hankel determinants on some classical combinatorial sequences such as Catalan numbers and polynomials, Bell polynomials, Hermite polynomials, Derangement polynomials etc. From a pair of matrices this paper introduces two kinds of numbers. Using the first kind of numbers we give a unified treatment of Hankel determinants on those sequences, i.e., to consider a general representation of Hankel matrices on the first kind of numbers. It is interesting that the Hankel determinant of the first kind of numbers has a close relation that of the second kind of numbers.


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