Alternate Sylvester sums on the Frobenius set

Authors:
Weiping Wang;Tianming Wang
Affiliations:
Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, PR China;Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, PR China
Venue:
Computers & Mathematics with Applications
Year:
2008

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Abstract

The alternate Sylvester sums are T"m(a,b)=@?"n"@?"N"R(-1)^nn^m, where a and b are coprime, positive integers, and NR is the Frobenius set associated with a and b. In this note, we study the generating functions, recurrences and explicit expressions of the alternate Sylvester sums. It can be found that the results are closely related to the Bernoulli polynomials, the Euler polynomials, and the (alternate) power sums over the natural numbers.