# Series Representation of Power Function

Abstract : In this paper we discuss a problem of generalization of binomial distributed triangle, that is sequence $\href{https://oeis.org/A287326}{A287326}$ in OEIS. The main property of $\href{https://oeis.org/A287326}{A287326}$ that it returns a perfect cube $n$ as sum of $n$-th row terms over $k, \ 0\leq k\leq n-1$ or $1\leq k\leq n$, 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 $n^{2m+1}, \ m\geq0$ as sum of row terms of corresponding triangle.
Keywords :
Type de document :
Pré-publication, Document de travail
16 pages, 8 figures, 2 tables, typos revised, added missing references, results generalized and s.. 2018
Domaine :

Littérature citée [25 références]

https://hal.archives-ouvertes.fr/hal-01283042
Contributeur : Petro Kolosov <>
Soumis le : mardi 29 mai 2018 - 23:02:40
Dernière modification le : jeudi 7 juin 2018 - 01:04:57

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SERIES REPRESENTATION REVISED ...
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### Citation

Kolosov Petro. Series Representation of Power Function. 16 pages, 8 figures, 2 tables, typos revised, added missing references, results generalized and s.. 2018. 〈hal-01283042v10〉

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