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Curious if this function is called anything.

by hddd123456789
Tags: called, curious, expansion, factorial, function, summation
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hddd123456789
#1
Dec24-13, 12:09 PM
P: 82
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
sum-function.jpg  
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hddd123456789
#2
Dec24-13, 12:51 PM
P: 82
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.
Pythagorean
#3
Dec24-13, 01:49 PM
PF Gold
Pythagorean's Avatar
P: 4,287
I don't know, but I think it could be simplified with pi notation:

http://en.wikipedia.org/wiki/Multipl...al_Pi_notation

hddd123456789
#4
Dec30-13, 03:08 PM
P: 82
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
sum-function.jpg  


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