# Curious if this function is called anything.

1. ### hddd123456789

90
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!

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10.5 KB
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52
2. ### hddd123456789

90
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.

Last edited: Dec 24, 2013

4,603
4. ### hddd123456789

90
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 Files:

• ###### sum-function.jpg
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15.7 KB
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24
Last edited: Dec 30, 2013