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The term "left factorial" is sometimes used to refer to the subfactorial.

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 $ n > 1 $.

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