sanity (Catalan numbers, r=1,d=1): nullity = 1
m_{2n}                       terms=154  recurrences found: none
      tested (order r, all degrees d <= dmax): [(1, 71), (2, 47), (3, 34), (4, 27), (5, 22), (6, 19), (7, 16), (8, 14), (9, 12), (10, 11), (11, 10), (12, 9), (13, 8), (14, 7)]
B_n = n! m_{2n}              terms=154  recurrences found: none
      tested (order r, all degrees d <= dmax): [(1, 71), (2, 47), (3, 34), (4, 27), (5, 22), (6, 19), (7, 16), (8, 14), (9, 12), (10, 11), (11, 10), (12, 9), (13, 8), (14, 7)]
m_{2n}/(2n)!                 terms=154  recurrences found: none
      tested (order r, all degrees d <= dmax): [(1, 71), (2, 47), (3, 34), (4, 27), (5, 22), (6, 19), (7, 16), (8, 14), (9, 12), (10, 11), (11, 10), (12, 9), (13, 8), (14, 7)]
n! m_{2n}/(2n)!              terms=154  recurrences found: none
      tested (order r, all degrees d <= dmax): [(1, 71), (2, 47), (3, 34), (4, 27), (5, 22), (6, 19), (7, 16), (8, 14), (9, 12), (10, 11), (11, 10), (12, 9), (13, 8), (14, 7)]
k_{2n} (Boolean cumulants)   terms=153  recurrences found: none
      tested (order r, all degrees d <= dmax): [(1, 71), (2, 46), (3, 34), (4, 27), (5, 22), (6, 18), (7, 16), (8, 14), (9, 12), (10, 11), (11, 10), (12, 9), (13, 8), (14, 7)]
n! k_{2n}                    terms=153  recurrences found: none
      tested (order r, all degrees d <= dmax): [(1, 71), (2, 46), (3, 34), (4, 27), (5, 22), (6, 18), (7, 16), (8, 14), (9, 12), (10, 11), (11, 10), (12, 9), (13, 8), (14, 7)]
k_{2n}/(2n-2)!               terms=153  recurrences found: none
      tested (order r, all degrees d <= dmax): [(1, 71), (2, 46), (3, 34), (4, 27), (5, 22), (6, 18), (7, 16), (8, 14), (9, 12), (10, 11), (11, 10), (12, 9), (13, 8), (14, 7)]
