Qmd1series[x_, rho_] :=
Module[{sum = 0, logrho, prev = 0, lf, fa = 1, n},
  For[n = Floor[x] + 1, n < x + 50, n++,
      sum += (rho(n-x))^n / n! * Exp[-rho n];
  ];
  sum  Exp[rho x] (1 - rho)
]