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Zbl 0859.11016
Howard, F.T.
Sums of powers of integers via generating functions. (English)
[J] Fibonacci Q. 34, No.3, 244-256 (1996). ISSN 0015-0517

The author uses generating functions to generalize some known formulas for the sums $$S_{k,n} (a,d)= a^k+(a+d)^k+ (a+2d)^k+ \cdots+ \bigl(a+ (n-1)d \bigr)^k$$ and $$T_{k,n} (a,d)=a^k-(a+d)^k+ (a+2d)^k- \cdots+ (-1)^{n-1} \bigl(a+(n-1)d \bigr)^k,$$ where $a$ and $d\ne 0$ are complex numbers, $k$ and $n\ne 0$ are nonnegative integers. In particular, recurrence relations and explicit formulas involving Bernoulli numbers are given.
[L.Tóth (Cluj)]

MSC 2000:: *11B57 Farey sequences
05A15 Combinatorial enumeration problems
11B68 Bernoulli numbers, etc.
11B37 Recurrences

Keywords: sums of powers of integers; generating functions; recurrence relations; Bernoulli numbers

Cited in: Zbl 0969.11012

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