The "TREE" sequence begins "TREE"(1) = 1, "TREE"(2) = 3, then suddenly "TREE"(3) explodes to a value so immensely large that many other "large" combinatorial constants, such as Friedman's "n"(4), are extremely small by comparison. In fact, it is much larger than "n""n"(5)(5). A lower bound for "n"(4), and hence an "extremely" weak lower bound for "TREE"(3), is "A""A"(187196)(1), where "A"() is a version of Ackermann's function: formula_4. Graham's number, for example, is approximately "A"64(4), which is much smaller than the lower bound "A""A"(187196)(1). It can be shown that the growth-rate of the function TREE is at least formula_5 in the fast-growing hierarchy. "A""A"(187196)(1) is approximately formula_6, where "g"x is Graham's function.