Is there an R function to get the number of permutations of n objects take k P(n,k)?

I don't know of any existing function. Your first suggestion will fail with large n. Your second idea should work fine when written as a function:

perm <- function(n,k){choose(n,k) * factorial(k)}

Then perm(500,2) will give 249500 for example.

I think the gregmisc package provides these functions.

library(gregmisc)
permutations(n=4,r=4)

Mailing list reference: [R] permutation

Check out nsamp(n,k,ordered=T) in the 'prob' package