Calkin, Neil J. Factors of sums of powers of binomial coefficients. (English) Zbl 0917.11011 Acta Arith. 86, No. 1, 17-26 (1998). The author shows that for all positive integers \(n\), \(m\), \[ \sum _{0\leq k \leq 2n} (-1)^k {{2n}\choose {k}}^m \] is divisible by \({2n}\choose{n}\). Reviewer: Y.O.Hamidoune (Paris) Cited in 2 ReviewsCited in 26 Documents MSC: 11B65 Binomial coefficients; factorials; \(q\)-identities 05A10 Factorials, binomial coefficients, combinatorial functions Keywords:binomial coefficients PDFBibTeX XMLCite \textit{N. J. Calkin}, Acta Arith. 86, No. 1, 17--26 (1998; Zbl 0917.11011) Full Text: DOI EuDML Online Encyclopedia of Integer Sequences: Array a(m,n) (m>0, n>=0) of quotient of de Bruijn alternating sums of m-th powers of binomial coefficients, listed by ascending antidiagonals.