All computations are in the S_n-invariant part.

When there are two lines, relation rank is first, Gorenstein rank second.
When there is just one line, the ranks are known to be equal.

-------------------------------------
n=0:
  g=2:  1   2   1
  g=3:  1   3   7  10   7
  g=4:  1   4  13  32  50  50
  g=5:  1   4  19  65 165 291 355   ?
        1
-------------------------------------
n=1:
  g=2:  1   3   5   3
  g=3:  1   5  16  29  29
  g=4:  1   6  30  93 191  240   ?
        1      30  93 191  240 191
  g=5:  1   7  44 197 624 1371   ?   ?
        1
-------------------------------------
n=2:
  g=2:  1   5  11  11
  g=3:  1   7  31  74 100  74
-------------------------------------
n=3:
  g=2:  1   6  20  28  20
-------------------------------------
n=4:
  g=2:  1   8  33  67  67
-------------------------------------
n=5:
  g=2:  1   9  49 128 181   ?
        1
-------------------------------------
n=6:
  g=2:  1  11  68 229   ?   ?
        1         229
-------------------------------------