E:=proc(P,M) local m,p,E,R:
E:=[[seq(0,m=1..M+1)]]:
for p from 2 to P+1 do
 R:=[p-1]: #begin the row
 for m from 2 to M+1 do
  R:=[op(R),1+((m-1)/(m+p-2))*R[m-1] + ((p-1)/(m+p-2))*E[p-1][m]]: #define the rest of the row
 od:
 E:=[op(E),R]: #Add the row to E
od:
E[P+1,M+1]:
end:

#ExpTim(110,100) = 209.1