An upper bound on binomial coefficients in the de Moivre – Laplace form - Agievich, Sergey V. (Journal of the Belarusian State University. Mathematics and Informatics, 2022)
We provide an upper bound on binomial coefficients that holds over the entire parameter range an whose form repeats the form of the de Moivre – Laplace approximation of the symmetric binomial distribution. Using the bound, we estimate the number of continuations of a given Boolean function to bent functions, investigate dependencies into the Walsh – Hadamard spectra, obtain restrictions on the number of representations as sums of squares of integers bounded in magnitude.