# Curious if this function is called anything.

by hddd123456789
Tags: called, curious, expansion, factorial, function, summation
 P: 76 Hey everyone, I was just playing around with factorial expansion and after grouping some terms I noticed a pattern for which I made a function. I am happy to provide more details as needed, but for now I have attached an image of the function and am curious, as per the title, whether this is known and if so if it has a name and/or interesting properties. I forgot to put this on the image but I was only considering positive naturals for a and n when defining the function. Thanks! Attached Thumbnails
 P: 76 Sorry, I should've posted this after working out the kinks. The a-n-1, a-n-2 part should be a-(n-1), a-(n-2), ... and k_n=n-1 should be k_n=n.
 PF Gold P: 4,212 I don't know, but I think it could be simplified with pi notation: http://en.wikipedia.org/wiki/Multipl...al_Pi_notation
P: 76

## Curious if this function is called anything.

Actually, I figured out that these are (unsigned) Stirling numbers of the first kind (save where n=0), with 'a' being the rows of its pyramid, and 'n' being the column in each row. Ironic that I called the function S. I attached a simpler (and more accurate) version for anyone interested.
Attached Thumbnails

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