The first, 22, terms   of the v-Series for the Free Energy are

[1, 3/2, 7/3, 19/4, 61/5, 75/2, 911/7, 3923/8, 17629/9, 81743/10, 388323/11, 
1880881/12, 9256677/13, 46169385/14, 232913767/15, 1186581075/16, 6096959765/17
, 3507139575/2, 164502941755/19, 862456678239/20, 649420014503/3, 
24077341257357/22]