TABLE 1.

Asymptotic constants β_t with h_n ~ β_tc_n, for seed trees t with 9 taxa.

Seed tree t	β t	${\beta }_t^{\ast }$	Seed tree t	β t	${\beta }_t^{\ast }$
	65,536	1		128,864	$\frac{4,027}{2,048}$
	81,920	$\frac{5}{4}$		166,624	$\frac{5,207}{2,048}$
	94,208	$\frac{23}{16}$		197,296	$\frac{12,331}{4,096}$
	104,448	$\frac{51}{32}$		224,704	$\frac{3,511}{1,024}$
	138,240	$\frac{135}{64}$		308,576	$\frac{9,643}{2,048}$
	118,784	$\frac{29}{16}$		262,000	$\frac{16,375}{4,096}$
	113,408	$\frac{443}{256}$		250,272	$\frac{7,821}{2,048}$
	148,480	$\frac{145}{64}$		339,504	$\frac{21,219}{4,096}$
	177,664	$\frac{347}{128}$		417,632	$\frac{13,051}{2,048}$
	141,312	$\frac{69}{32}$		326,240	$\frac{10,195}{2,048}$
	193,536	$\frac{189}{64}$		464,128	$\frac{1,813}{256}$
	121,472	$\frac{949}{512}$		182,912	$\frac{1,429}{512}$
	157,888	$\frac{2,467}{1,024}$		243,904	$\frac{3,811}{1,024}$
	187,776	$\frac{1,467}{512}$		296,064	$\frac{2,313}{512}$
	214,720	$\frac{3,355}{1,024}$		344,512	$\frac{5,383}{1,024}$
	296,192	$\frac{1,157}{256}$		487,808	$\frac{3,811}{512}$
	251,136	$\frac{981}{256}$		410,112	$\frac{801}{128}$
	162,560	$\frac{635}{256}$		214,016	$\frac{209}{64}$
	219,136	$\frac{107}{32}$		306,112	$\frac{4,783}{1,024}$
	268,288	$\frac{131}{32}$		294,784	$\frac{2,303}{512}$
	177,664	$\frac{347}{128}$		425,216	$\frac{1,661}{256}$
	249,344	$\frac{487}{128}$		366,720	$\frac{2,865}{512}$
	353,536	$\frac{1,381}{256}$		532,224	$\frac{2,079}{256}$

Values of β_t appear for each of the 46 unlabeled species trees with 9 taxa. For each species tree t, we also provide the constant ${\beta }_t^{\ast }={\beta }_t∕4^8$ (eq. (40)). Trees are listed in increasing order by rank as defined in Section 2 of [14]. In the left column, each seed tree t belongs to a caterpillar-like family (t̃⁽ⁿ⁾)n, with |t̃| < 9. In these cases, we recover the values of ${\beta }_t^{\ast }$ as determined in Table 3 of [14].