Expansion in high dimension for the growth constants of lattice trees   and lattice animals
  We compute the first three terms of the 1/d expansions for the growth constants and one-point functions of nearest-neighbour lattice trees and lattice (bond) animals on the integer lattice Zd, with rigorous error estimates. The proof uses the lace expansion, together with a new expansion for the one-point functions based on inclusion-exclusion. 
Yuri Mejia Miranda and Gordon Slade
math.PR