sanity (Catalan numbers, r=1,d=1): nullity = 1
m_{2n}                       terms=101  recurrences found: none
      tested (order r, all degrees d <= dmax): [(1, 45), (2, 29), (3, 21), (4, 16), (5, 13), (6, 11), (7, 9), (8, 8), (9, 7), (10, 6), (11, 5), (12, 5)]
B_n = n! m_{2n}              terms=101  recurrences found: none
      tested (order r, all degrees d <= dmax): [(1, 45), (2, 29), (3, 21), (4, 16), (5, 13), (6, 11), (7, 9), (8, 8), (9, 7), (10, 6), (11, 5), (12, 5)]
m_{2n}/(2n)!                 terms=101  recurrences found: none
      tested (order r, all degrees d <= dmax): [(1, 45), (2, 29), (3, 21), (4, 16), (5, 13), (6, 11), (7, 9), (8, 8), (9, 7), (10, 6), (11, 5), (12, 5)]
n! m_{2n}/(2n)!              terms=101  recurrences found: none
      tested (order r, all degrees d <= dmax): [(1, 45), (2, 29), (3, 21), (4, 16), (5, 13), (6, 11), (7, 9), (8, 8), (9, 7), (10, 6), (11, 5), (12, 5)]
k_{2n} (Boolean cumulants)   terms=100  recurrences found: none
      tested (order r, all degrees d <= dmax): [(1, 44), (2, 29), (3, 21), (4, 16), (5, 13), (6, 11), (7, 9), (8, 8), (9, 7), (10, 6), (11, 5), (12, 5)]
n! k_{2n}                    terms=100  recurrences found: none
      tested (order r, all degrees d <= dmax): [(1, 44), (2, 29), (3, 21), (4, 16), (5, 13), (6, 11), (7, 9), (8, 8), (9, 7), (10, 6), (11, 5), (12, 5)]
k_{2n}/(2n-2)!               terms=100  recurrences found: none
      tested (order r, all degrees d <= dmax): [(1, 44), (2, 29), (3, 21), (4, 16), (5, 13), (6, 11), (7, 9), (8, 8), (9, 7), (10, 6), (11, 5), (12, 5)]
