Distribution Probabilities

If your opponents have between them exactly n trumps, what are the chances that your opponent on the left has exactly k of them ?

k n=2 n=3 n=4 n=5 n=6 n=7 n=8 n=9 n=10
0 0.236842 0.105263 0.043344 0.016254 0.005418 0.001548 0.000357 0.000060 0.000005
1 0.526316 0.394737 0.247678 0.135449 0.065015 0.027090 0.009526 0.002679 0.000541
2 0.236842 0.394737 0.417957 0.348297 0.243808 0.146285 0.075018 0.032151 0.010960
3   0.105263 0.247678 0.348297 0.371517 0.325077 0.240057 0.150036 0.077941
4     0.043344 0.135449 0.243808 0.325077 0.350083 0.315075 0.238693
5       0.016254 0.065015 0.146285 0.240057 0.315075 0.343718
6         0.005418 0.027090 0.075018 0.150036 0.238693
7           0.001548 0.009526 0.032151 0.077941
8             0.000357 0.002679 0.010960
9               0.000060 0.000541
10                 0.000005

Here is the same table "folded", i.e., the probabilities that the hand with smaller number of trumps has exactly k of them:

k n=2 n=3 n=4 n=5 n=6 n=7 n=8 n=9 n=10
0 0.473684 0.210526 0.086687 0.032508 0.010836 0.003096 0.000714 0.000119 0.000011
1 0.526316 0.789474 0.495356 0.270898 0.130031 0.054180 0.019052 0.005358 0.001083
2     0.417957 0.696594 0.487616 0.292570 0.150036 0.064301 0.021921
3         0.371517 0.650155 0.480114 0.300071 0.155881
4             0.350083 0.630150 0.477386
5                 0.343718