I know just enough math and also just enough r to give you the implementation of the common definition
as seen here:
the n-th harmonic number is the sum of the reciprocals of the first n natural numbers
Harmonic number - Wikipedia
harmonicnumber <- function(n){
k <- seq_len(n)
-sum((-1)^k*(1/k) * choose(n,k))
}
This doesn't cover -3/4 as that is not a natural number