MathDB

2009 Combinatorics #10 - Rearrangement of First n Integers

Source:

January 7, 2012

Problem Statement

Given a rearrangement of the numbers from

1

n

, each pair of consecutive elements

a

and

b

of the sequence can be either increasing (if

a < b

) or decreasing (if

b < a

). How many rearrangements of the numbers from

1

n

have exactly two increasing pairs of consecutive elements? Express your answer in terms of

n