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question for compiling a function


Hello,

I am doing some MCMC on mathematica and performance is becoming an
issue.  So the low hanging fruit would be compiling some functions.
Below is an portion of the key one:

example[n_, \[Alpha]_] :=
 Gamma[Plus @@ n + \[Alpha]]/Times @@ (Gamma[# + 1] & /@ n)

"n" is a vector of positive reals.  However, I don't know how big it
is, it will usually be just 4 o 5 numbers but could be anything from 1
to 200 size vector.

Any suggestions?

Thanks in advance,
Ramiro


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