[math-fun] strong law of small numbers ? surely not!

the count of plane partitions of n that can be extended in exactly 3 ways to a plane partition of n+1 by adding one element equals Anum=A007425 = 1,3,3,6,3,9,3,10,6,9,3,18,3,9,9,15 .. or Inverse Moebius transform applied twice to all 1's sequence. or tau_3(n) *** the count of solid partitions of n that can be extended in exactly 4 ways to a solid partition of n+1 by adding one element equals Anum=A007426 1,4,4,10,4,16,4,20,10,16 .. or Inverse Moebius transform applied thrice to all 1's sequence or tau_4(n) *** ?? duh? W.