On an explicit representation of central $(2k+1)$-nomial coefficients
arXiv:1403.5942v1 [math.CO], 2014
arXiv:1403.5942v1 [math.CO], 2014
Abstract
We propose an explicit representation of central $(2k+1)$-nomial coefficients in terms of finite sums over trigonometric constructs. The approach utilizes the diagonalization of circulant boolean matrices and is generalizable to all $(2k+1)$-nomial coefficients, thus yielding a new family of combinatorical identities.