MathDB

An ancient noble family has

n

members, each holding a different number of posts . As every year in December, they gather at a very specific place for a Council of War to be held, where also k, from the point of view of the high nobility, unimportant spammers speak up, which, due to their irrelevance, should and cannot be further differentiated. The Council is held as follows: those present speak one after the other, each one carefully put forward his request once. In addition, for reasons of respect, a nobleman never speaks right after a nobleman who holds more posts, while the common people disregarde such rules. Find the number of possible sequences of the Council of war.

Problem Statement