Let T(x, y, z) be the number of times "otherwise" is called in the TAK function, then the Takeuchi numbers are defined by T_n(n, 0, n + 1). A recursive formula for T_n is given by T_n = sum_(k = 0)^(n - 2)[2(n + k - 1 k) - (n + k k)] t_(n - k - 1) + sum_(k = 1)^n C_n, where C_n is a Catalan number. The values for n = 0, 1, ... are 0, 1, 4, 14, 53, 223, 1034, 5221, 28437, ... (OEIS A000651).

Takeuchi-Prellberg constant | TAK function