Telephone Numbers

Telephone Numbers

Spiked Math Comic - Telephone Numbers

Relevant link: http://en.wikipedia.org/wiki/Telephone_number_(mathematics)

Also called the involution numbers, they can be determined by the recurrence:

      a_0 = a_1 = 1;
      a_n = a_{n−1} + (n − 1) a_{n−2}, for n > 1.

More interesting, they also count the number of involutions on a set with n elements — note that an involutary function, is a function f that is its own inverse, that is,

     f(f(x)) = x for all x in the domain of f.

(Via Spiked Math.)