Problem with RecurrenceTable of two variables

Question

Let we have simple recursive function:

Clear[recFun];
recFun[1, k_] := 1;
recFun[n_, 1] := 1;
recFun[n_, k_] := recFun[n, k - 1] + recFun[n - 1, k - 1];
recFun[2,3]
Out: 3

But this code not work:

Clear[rf]; RecurrenceTable[{rf[n, k] == rf[n, k - 1] + rf[n - 1, k - 1], 
      rf[1, k] == 1, rf[n, 1] == 1}, rf, {n, 1, 3}, {k, 1, 3}]

I've read this topic, but TS was answered how to do recursion. Why RecurrenceTable not work remained unclear.

Answer 1

This works:

Clear[rf]; 
RecurrenceTable[{rf[n, k] == 
    If[k >= 2 && n >= 2, rf[n, k - 1] + rf[n - 1, k - 1], 1], 
   rf[n, 1] == 1, rf[1, k] == 1}, rf, {n, 1, 5}, {k, 1, 5}] // Grid

1   1   1   1   1
1   2   3   4   5
1   2   4   7   11
1   2   4   8   15
1   2   4   8   16

---

This doesn't work:

Clear[rf];
RecurrenceTable[{rf[n, k] == 
    If[k >= 2 && n >= 2, rf[n, k - 1] + rf[n - 1, k - 1], 1], 
   rf[1, k] == 1, rf[n, 1] == 1}, rf, {n, 1, 5}, {k, 1, 5}] // Grid