Finch, S. R. Mathematical Constants. Cambridge, England: Cambridge University Press, p. 321, 2003.Knuth,
D. E. "Textbook Examples of Recursion." Artificial
Intelligence and Mathematical Theory of Computation, Papers in Honor of John McCarthy
(Ed. V. Lifschitz). Boston, MA: Academic Press, pp. 207-229, 1990.Lifschitz,
V. (Ed.). Artificial Intelligence and Mathematical Theory of Computation. Papers
in Honor of John McCarthy. Boston, MA: Academic Press, p. 215, 1991.Prellberg,
T. "On the Asymptotics of Takeuchi Numbers." In Symbolic Computation,
Number Theory, Special Functions, Physics and Combinatorics. Dordrecht, Netherlands:
Kluwer, pp. 231-242, 2001.Sloane, N. J. A. Sequence
A000651 in "The On-Line Encyclopedia of
Integer Sequences."
be the number of times "otherwise" is called in the TAK
function, then the Takeuchi numbers are defined by 
.
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)^nC_n,](/images/equations/TakeuchiNumber/NumberedEquation1.svg)
is a Catalan number. The values for 
, 1, ... are 0, 1, 4, 14, 53, 223, 1034, 5221, 28437, ...
(OEIS A000651).
