Abstract
In this paper, we present two explicit expressions of the moments M2k of the Kesten distribution in terms of Catalan's triangles Tk,i=k−i+1k+1(k+ik) and Shapiro's Catalan triangles Bk,j=jk(2kk−j), respectively. As a corollary, we provide a generalization of the identity, due to Eplett, between the Catalan number Ck=1k+1(2kk) and the triangles Bk,j. As an application, we obtain an asymptotic formula on M2k as k tends to infinity.
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