Closed-form of infinite continued fraction involving factorials

Question

Is there a closed form of this:

$$ 1!+\dfrac{1}{2!+\dfrac{1}{3!+\dfrac{1}{4!+\ldots}}} $$

Answer 1

My 2 cents worth. Here is a Pascal program snippet that does Peter's job; actually half of it due to Delphi's double precision limitations. Backward recursion is the clue (again).

program Peter;

procedure fraction;
var
  a : double;
  f,k : integer;
begin
  f := 1*2*3*4*5*6*7*8*9*10;
  k := 10; a := f;
  while k > 1 do
  begin
    f := f div k;
    a := 1/a+f;
    k := k-1;
  end;
  Writeln(a);
end;

begin
  fraction;
end.

Output:

 1.46178335500058E+0000

Closed form? I don't think so.