Approximate the Fransén-Robinson constant Given an input n, output the value of the Fransén-Robinson constant with n digits after the decimal place, with rounding.

Rules


You may assume that all inputs are integers between 1 and 60.
You may not store any related values - the constant must be calculated, not recalled.
Rounding must be done with the following criteria:


If the digit following the final digit is less than five, the final digit must remain the same.
If the digit following the final digit is greater than or equal to five, the final digit must be incremented by one.

You must only output the first n+1 digits.
Standard loopholes apply.


Test Cases

&gt;&gt;&gt; f(0)
3

&gt;&gt;&gt; f(1)
2.8

&gt;&gt;&gt; f(11)
2.80777024203

&gt;&gt;&gt; f(50)
2.80777024202851936522150118655777293230808592093020

&gt;&gt;&gt; f(59)
2.80777024202851936522150118655777293230808592093019829122005

&gt;&gt;&gt; f(60)
2.807770242028519365221501186557772932308085920930198291220055
Mathematica, 44 39 36 25 UTF-8 bytes


-5 bytes thanks to Sp3000 
-3 bytes thanks to kennytm
-11 bytes thanks to senegrom


Crossed out 44 is still regular 44!!

N[∫1/x!{x,-1,∞},#+1]&amp;


Example:

f=N[∫1/x!{x,-1,∞},#+1]&amp;
f[2]


Outputs 2.81.

Explanation

N[               , # + 1] 
  ∫1/x!{x,-1,∞}


First step takes Numeric of the rest, with # (first parameter) + 1 precision. ! (factorial) does what you'd expect. {x, -1, Infinity} sets the bounds for the (strangely formatted) Integral.