The numbers 
,
where 
is a Hermite polynomial, may be called Hermite
numbers. For 
,
1, ..., the first few are 1, 0, 
, 0, 12, 0, 
, 0, 1680, 0, ... (OEIS A067994).
They are given explicitly by
 |  |  |
(1)
|
 |  |  |
(2)
|
As a result of the ratio 
always being divisible by 
for 
, the only prime Hermite number is 
.
The Hermite numbers 
are related to the Hermite polynomials 
by
 |
(3)
|
where 
,
and
 |
(4)
|
where 
.
