
#1
Dec2413, 12:09 PM

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! 



#2
Dec2413, 12:51 PM

P: 76

Sorry, I should've posted this after working out the kinks. The an1, an2 part should be a(n1), a(n2), ... and k_n=n1 should be k_n=n.




#3
Dec2413, 01:49 PM

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 



#4
Dec3013, 03:08 PM

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.



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