I'm trying to figure out if a generating function exists for the equation (x + n)! / x!. Like, a way to convert it into polynomial form for any n. Not really urgent, but it would be pretty convenient if anyone has any leads.
#Generating Function for Factorial-Related Equation?
paper bear
kindred scrollBOT
glossy latch
I'm trying to figure out if a generating function exists for the equation `(x + ...
wouldn't that just be (x+1)(x+2)...(x+n)?
paper bear
specifically i want way to convert it into the form $a + a_1 x + a_2 x^2 + ... + a_n x^n$
amber hedgeBOT
Yokin
paper bear
i could multiply the (x+1)(x+2)...(x+n) out manually, but it really is just about the convenience
glossy latch
looked around on the internet a little and it looks like there is a formula for the coefficients involving stirling numbers of the first kind
paper bear
thanks, i'll look into it
glossy latch
actually that might be for something else 😞
