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The purpose of this paper is to construct a new family of the special numbers which are related to the Fubini type numbers and the other well-known special numbers such as the Apostol-Bernoulli numbers, the Frobenius-Euler numbers and the Stirling numbers. We investigate some fundamental properties of these numbers and polynomials. By using generating functions and their functional equations, we derive various formulas and relations related to these numbers and polynomials. In order to compute the values of these numbers and polynomials, we give their recurrence relations. We give combinatorial sums including the Fubini type numbers and the others. Moreover, we give remarks and observation on these numbers and polynomials.
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참고문헌 (34)
참고문헌 신청
M. Alkan / 2013 / Generating function for q-Eulerian polynomials and their decomposition and applications / Fixed Point Theory Appl 2013(72):14
T. Apostol / 1951 / On the Lerch zeta function / Pacific J. Math 1(2):161~167
A. Bayad / 2014 / Some array type polynomials associated with special numbers and polynomials / Appl. Math. Comput 244:149~157
H. Belbachir / 2011 / Sums involving moments of reciprocals of binomial coefficients / J. Integer Seq 14(6):16
M. Bona / 2007 / Introduction to Enumerative Combinatorics / The McGraw-Hill Companies, Inc
T. Apostol / 1951 / On the Lerch zeta function / Pacific J. Math 1(2):161~167
A. Bayad / 2014 / Some array type polynomials associated with special numbers and polynomials / Appl. Math. Comput 244:149~157
H. Belbachir / 2011 / Sums involving moments of reciprocals of binomial coefficients / J. Integer Seq 14(6):16
M. Bona / 2007 / Introduction to Enumerative Combinatorics / The McGraw-Hill Companies, Inc
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