Number of distinct functions f representable as x -> x^x^...^x with n x's and parentheses inserted in all possible ways giving result f(0)=0, with conventions that 0^0=1^0=1^1=1, 0^1=0.

A222379

Number of distinct functions f representable as x -> x^x^...^x with n x's and parentheses inserted in all possible ways giving result f(0)=0, with conventions that 0^0=1^0=1^1=1, 0^1=0.