I am using Scala. This is the solution I found. It uses local mutation but it works. If you know how to make it more functional, please share:

def getTable(n: Int = 1001, k: Int = 1001): Array[Array[Long]] = {
  val mutableTable: mutable.ArrayBuffer[Array[Long]] = collection.mutable.ArrayBuffer()
  mutableTable += 1L +: Array.fill(n-1)(0L)
  for (i <- 1 until k) {
    val a1 = mutableTable(i-1) :+ 0L
    val a2 = 0L +: mutableTable(i-1)
    mutableTable += (0 until n).map( e => (a1(e) + a2(e)) % modulo).toArray
  }
  mutableTable.toArray
}

    [...]
val table = getTable()
    [...]
println(table(N)(K))