Consider m natural numbers n1, n2, …, nm with the property n1³ n2³ …³ nm>0.
We define a Young table as an arrangement in a table of n1+n2+…+nm natural numbers (bigger than 0 and any two different), so that the ith line has ni elements (1£ i£ m) in ascending order from left to right, and the elements from the same column are in ascending order from bottom to top.
An example of Young table for m=4, n1=6, n2=4, n3=4, n4=1 is the following:
1
2
5
9
10
15
3
6
7
13
4
8
12
14
11
Task:
Given n1, n2, …, nm determine the number of Young tables containing the elements 1, 2, …, n1+n2+…+nm.
