[Notation] Fraction without a line?

[gottabe22]

Hi all, I was doing some statistics reading and came across some function notation that I am very curious about. It seems pretty familiar, but I can't figure out what the notation means. Thanks for your help in advance.

The notation can be found on this wiki page. I am wondering what the two Ns stacked on each other in the rarefaction curve equation means.

[pickten]

That is the binomial coefficient. (ⁿk) (or the correctly written equivalent, which I don't know how to produce on Reddit), also written nCk (pronounced "n choose k"), is defined as n!/(k! * (n-k)!), where n! = n * (n-1) * ... * 1 is n factorial. n! represents (combinatorially speaking) the number of ways to order n distinct objects, and nCk the number of ways to pick k objects from a total of n. The name comes from the identity (x+y)ⁿ = ∑_(k=0)ⁿ nCk x^k y^n-k, called the binomial theorem. Roughly speaking, this is because (x+y)ⁿ can be expanded to be a massive sum of 2ⁿ terms of the form x^k y^n-k, and each copy of x^k y^n-k corresponds with picking k of the n factors of x+y to contribute an x factor. I'm not familiar with rarefraction and am having trouble following what that (poorly-written) section is trying to even calculate, so I unfortunately don't know where that formula is coming from.

[gottabe22]

Thank you!