A Remarkable Sequence of Integers
نویسنده
چکیده
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. 1. A quartic integral The problem of explicit evaluation of definite integrals has been greatly simplified due to the advances in symbolic languages like Mathematica and Maple. Some years ago the first author described in [26] how he got interested in these topics and the appearance of the sequence of rational numbers (1.1) d l,m = 2 −2m m k=l 2 k 2m − 2k m − k m + k m k l , for 0 ≤ l ≤ m. These are rational numbers with a simple denominator. The numbers 2 2m d l,m are the remarkable integers in the title. These rational coefficients d l,m appeared in the evaluation of the quartic integral
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