Consider m natural numbers n1, n2, …, nmwith the property n1³n2³…³ nm>0.
We define a Young table as an arrangement in a table of n1+n2+…+nmnatural numbers (bigger than 0 and any two different), so that the ithline has nielements (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:
Given n1, n2, …, nmdetermine the number of Young tables containing the elements1, 2, …, n1+n2+…+nm.
on the first line is: the natural number m;
on the second line are: the numbers n1, n2, …, nmseparated by a space.
contain the number of Young tables that can be built.