A remarkable sequence of integers

A survey of properties of a sequence of coefficients appearing in the evaluation of a quartic definite integral is presented. These properties are of analytical, combinatorial and number-theoretical nature.Comment: 20 pages, 5 figure

An Extension of a Criterion for Unimodality

We prove that if P(x) is a polynomial with nonnegative nondecreasing coefficients and n is a positive integer, then P(x+n) is unimodal. Applications and open problems are presented