IJPAM: Volume 28, No. 2 (2006)

ON A TRIANGULAR INVERSION FORMULA,
ITS APPLICATION AND ORDERED BELL NUMBERS

Pavel Trojovský
Faculty of Economics and Administration
Institute of Mathematics
University of Pardubice
Studentská 84, Pardubice, 532 10, CZECH REPUBLIC
e-mail: pavel.trojovsky@uhk.cz


Abstract.The paper is devoted to the deriving a general triangular inverse formula between any sequences $\{x_n\}$ and $\{y_n\}$ and an explicit formula for triangular sequence $\{x_n\}$. Further it is shown a way of using this closed form for finding relation for any sequence which is connected with the ordered Bell numbers. For this purpose we derive some new identities for the ordered Bell numbers, too.

Received: August 25, 2005

AMS Subject Classification: 05A19, 05A10, 05A18, 11B73

Key Words and Phrases: inversion formulas, triangular sequences, Bell numbers, ordered Bell numbers, Stirling numbers

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 28
Issue: 2