I'm stuck in a problem and need help. Associative law states that
(a + b) + c = a + (b + c)
If there are 4 elements, there are 5 arrangements satisfying the property.
(a + b) + (c + d)
((a + b) + c) + d
(a + (b + c)) + d
a + ((b + c) + d)
a + (b + (c + d))
I counted the total number of possible arrangements for 5 elements, which is 14.
n = 2 #of arrangements = 1
n = 3 #of arrangements = 2
n = 4 #of arrangements = 5
n = 5 #of arrangements = 14
Is there a way to calculate the total number of arrangements satisfying the associative property for n elements?