Geodesic
Combinatorial representation of the sum of the weighted equal powers of members of an arithmetical progression
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 4 (2013), pp. 184-191.

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The correctness of equality which gives the combinatorial expression for the sum of the weighted equal powers of members of an arithmetical progression is found out. Such aspect provides usage of double summation of certain algebraic combinations with free and weight components of the given sum. Thus specified algebraic combinations also include binomial coefficients. Determination of required equality was made with use of comparison of real and hypothetical values.
Keywords: sum of the weighted equal powers, real representation, hypothetical representation
Mots-clés : binomial coefficients. 
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A. I. Nikonov. Combinatorial representation of the sum of the weighted equal powers of members of an arithmetical progression. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 4 (2013), pp. 184-191. http://geodesic.mathdoc.fr/item/VSGTU_2013_4_a15/

[1] A. I. Nikonov, “Converting the Sum of Weighted Degrees of Natural Numbers with the Same Parameters”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 1(20) (2010), 258–262 | DOI

[2] A. I. Nikonov, “On One Property of the Weighed Sums of Equal Powers as Matrix Products”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 5(21) (2010), 313–317 | DOI

[3] A. I. Nikonov, “Reduction of the sum of the weight equal powers to explicit combinatorial representation”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 3(28) (2012), 163–169 | DOI | Zbl

[4] A. I. Nikonov, Discrete Mathematics, Samara State Technical Univ., Samara, 2011, 106 pp.