Number Theory


Series Representation of Power Function

Authors: Kolosov Petro

In this paper we discuss a problem of generalization of binomial distributed triangle, that is sequence A287326 in OEIS. The main property of A287326 that it returns a perfect cube n as sum of n-th row terms over k, 0 <= k <= n-1 or 1 <= k <= n, by means of its symmetry. In this paper we have derived a similar triangles in order to receive powers m=5,7 as row items sum and generalized obtained results in order to receive every odd-powered monomial n^{2m+1}, m <= 0 as sum of row terms of corresponding triangle.

Comments: 16 pages, 8 figures, 2 tables, typos revised, added missing references, results generalized and shortened, derivations detailed

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Submission history

[v1] 2017-06-09 07:24:09
[v2] 2017-08-01 15:52:40
[v3] 2017-09-07 17:27:09
[v4] 2017-11-23 17:13:00
[v5] 2018-01-12 03:38:22
[v6] 2018-02-17 19:34:49
[v7] 2018-05-08 23:57:08
[v8] 2018-05-26 16:38:25

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