Dr. Alissa S. Crans presented the talk “A Surreptitious Sequence: The Catalan Numbers” in the Distinguished Lecture Series at the Carriage House of the Mathematical Association of America on May 21, 2014.
Abstract: Many of us are familiar with famous sequences of numbers such as the odd numbers 1, 3, 5, 7, …; perfect squares 1, 4, 9, 16, 25, …; Fibonacci sequence 1, 1, 2, 3, 5, 8, …; or the triangular numbers 1, 3, 6, 10, 15, … But what about the sequence 1, 1, 2, 5, 14, …? First described by Euler in the 1700s and made famous by Belgian mathematician Eugène Catalan 100 years later, these “Catalan numbers” take on a variety of different guises as they provide the solution to numerous problems throughout mathematics.
