I am supposed to write a function for Stirling Numbers of the Second Kind, given by the formula:

For this, I have written the following function in R:

stirling <- function(n, k)
{
  sum = 0
  for (i in 0:k)
  {
    sum = sum + (-1)^(k - i) * choose(k, i) * i^n
  }
  sum = sum / factorial(k)
  return(sum)
}

The next part of the question is to "create a plot for n = 20, k = 1,2,...,10". I did some research and I think the methods curve or plot might help me. However, I am guessing these methods are used when y is of the form f(x) (ie a single argument). But here, I have two arguments ( n and k ) in my function stirling so I am not sure how to approach this.

Also, I tried converting the values of k (0, 1, 2..., 10) to a vector and then passing them to stirling , but stirling won't accept vectors as input. I am not sure how to modify the code to make stirling accept vectors.

Any suggestions?

---

Vectorize

As pointed out in the comments, you can vectorize to do this:

Vectorize creates a function wrapper that vectorizes the action of its argument FUN. Vectorize(FUN, vectorize.args = arg.names, SIMPLIFY = TRUE, USE.NAMES = TRUE)

(vstirling <- Vectorize(stirling))
# function (n, k) 
# {
# args <- lapply(as.list(match.call())[-1L], eval, parent.frame())
# names <- if (is.null(names(args))) 
#     character(length(args))
# else names(args)
# dovec <- names %in% vectorize.args
# do.call("mapply", c(FUN = FUN, args[dovec], MoreArgs = list(args[!dovec]), 
#    SIMPLIFY = SIMPLIFY, USE.NAMES = USE.NAMES))
# }

so vstirling() is the vectorized version of stirling() .

vstirling(20, 1:10)
 # [1] 1.000000e+00 5.242870e+05 5.806064e+08 4.523212e+10 7.492061e+11 4.306079e+12 1.114355e+13 1.517093e+13
 # [9] 1.201128e+13 5.917585e+12

Now all that is left is creating a plot:

plot(x = 1:10, y = vstirling(20, 1:10), ylab = "S(20, x)", xlab = "x")

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