Catalan's constant

Catalan's constant is a constant that crops up regularly in combinatorial problems, especially in the evaluation of certain infinite series and integrals. For example, it is equal to


integral arctan(x) / x dx, and


1 - (1/3)2 + (1/5)2 - (1/7)2 + (1/9)2 - ...


It is also the solution to the following problem as n becomes arbitrarily large: If you have a 2n × 2n checkerboard and a supply of 2n2 dominoes that are just large enough to cover two squares of the checkerboard, how many ways are there to cover the whole board with the dominoes? Catalan's constant has the value 0.915965...; it is not known if it is an irrational number.