v
=# ways to “parenthesize” (n+1) objects
v Matrix Power Term Graph
v(1((23)4)) A12A23A32A24A42A21
v(((12)3)4) A12A21A13A31A14A41
v(1(2(34))) A12A23A34A43A32A21
v((12)(34)) A12A21A13A34A43A31
v((1(23))4) A12A23A32A21A14A41
v= number of special paths on n departing from 1
once
vPass 1,
(load=advance, multiply=retreat), Return to 1
v
v
v
v