For positive integers n and p, we give a short proof of a formula expressing np as a linear combination of figurate numbers with coefficients given by the numbers (Formula presented.) of (Formula presented.) -dimensional facets of p-dimensional simplices obtained by cutting a p-dimensional cube, where (Formula presented.). This formula was formulated as Conjecture 16 in F. Marko and S. Litvinov (2020), Geometry of figurate numbers and sums of powers of consecutive natural numbers, this Monthly, 127(1): 4–22.
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