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Omni-MATH / Given a rearrangement of the numbers from 1 to 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 rea…

Problem

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problem

Given a rearrangement of the numbers from 1 to nn, each pair of consecutive elements aa and bb of the sequence can be either increasing (if a<ba<b ) or decreasing (if b<ab<a ). How many rearrangements of the numbers from 1 to nn have exactly two increasing pairs of consecutive elements?
Plain-text mathematical notation (without MathML)
Given a rearrangement of the numbers from 1 to 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 to n have exactly two increasing pairs of consecutive elements?
Original LaTeX notation
Given a rearrangement of the numbers from 1 to $n$, 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 to $n$ have exactly two increasing pairs of consecutive elements?

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Source and history

task_id
8d4ee838-9c55-52ae-81e2-0619d03bf5df
task_key
test--8d4ee838-9c55-52ae-81e2-0619d03bf5df
task_revision_id
1
config / split
/ test

Official source

initial import