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 n2m+1; m ≥ 0 as sum of row terms of corresponding triangle. In other words, in this manuscript are found and discussed the polynomials Dm(n,k) and Um(n,k), such that, when being summed up over k in some range with respect to m and n returns the monomial n2m+1.
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Subject: Computer Science and Mathematics - Algebra and Number Theory
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