You start a rumor by telling it to n people and each of them tells it to another n-1 people. If each of these people, in turn, tells the rumor to another n-2 people, and so forth with no person hearing the rumor from more than one source, find a closed-form expression (in terms of n) for the total number of people that have been told the rumor.
(In reply to re: computer aided solution (spoiler)
by Dej Mar)
The sixth paragraph of Sloane's A007526 has the caption "FORMULA", the first line of which contains the following text:
"a(n) = [ e*n! - 1 ] (J. K. Horn)."
Edited on January 7, 2009, 12:17 pm