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In this paper we consider the hypersum polynomials, P (m) k (n) = k+m+1 r=0 c r k,m n r , and give an explicit formula for the coefficients c r k,m. We show that the c r k,m 's satisfy a generalized Akiyama-Tanigawa recurrence relation, thus extending some previous results due to Inaba. We also give a number of identities involving the Stirling numbers of… (More)

Relying on a recurrence relation for the hypersums of powers of integers put forward recently, we develop an iterative procedure which allows us to express a hypersum of arbitrary order in terms of ordinary (zeroth order) power sums. Then, we derive the coefficients of the hypersum polynomial as a function of the Bernoulli numbers and the Stirling numbers… (More)

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