The term "left factorial" is sometimes used to refer to the subfactorial 
, the first few values for 
, 2, ... are 1, 3, 9, 33, 153, 873, 5913, ... (OEIS A007489).
Unfortunately, the same term and notation are also applied to the factorial sum
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
 |  |  |
(4)
|
where 
is a gamma function, 
is the exponential
integral, and 
is the En-function.
For 
,
1, ..., the first few values are given by 0, 1, 2, 4, 10, 34, 154, 874, ... (OEIS
A003422). The left factorial is always even
for 
.
is prime for 
, 4, 5, 8, 9, 10, 11, 30, 76, 163, 271, 273, 354, 721, 1796,
3733, 4769, 9316, 12221, ... (OEIS A100614),
the last of which was found by E. W. Weisstein (Oct. 19, 2006).
." Math. Balkanica 1, 147-153, 1971.Kurepa,
D. "Left Factorial Function in Complex Domain." Math. Balkanica 3,
297-307, 1973.Sloane, N. J. A. Sequences