CENTRAL LAH NUMBERS AND CENTRAL LAH-BELL NUMBERS
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초록
The central factorial numbers of the second kind appear in the expansion of powers of x in terms of the central factorials. Central factorial numbers are equally important as Stirling numbers and often arise in properties and applications for difference calculus, spline theory, and approximation theory, etc. This paper begins with the question of the form central Lah numbers and central Lah-Bell numbers comprise of, based upon our observations of the relation between central factorial numbers and the central Bell polynomials. With in this mind, the central Lah numbers and the central Lah-Bell numbers are introduced parallel to the central factorial numbers of the second kind and central Bell polynomials. We investigate several combinatorial identities of these numbers including the generating functions, explicit formulas, binomial convolutions, and represented by the Riemann integral, respectively.
Abstract
The central factorial numbers of the second kind appear in the expansion of powers of x in terms of the central factorials. Central factorial numbers are equally important as Stirling numbers and often arise in properties and applications for difference calculus, spline theory, and approximation theory, etc. This paper begins with the question of the form central Lah numbers and central Lah-Bell numbers comprise of, based upon our observations of the relation between central factorial numbers and the central Bell polynomials. With in this mind, the central Lah numbers and the central Lah-Bell numbers are introduced parallel to the central factorial numbers of the second kind and central Bell polynomials. We investigate several combinatorial identities of these numbers including the generating functions, explicit formulas, binomial convolutions, and represented by the Riemann integral, respectively.
참고문헌 (23)
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