Hermite numbers are the values 
, where 
is a physicists' Hermite
polynomial. 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 even integers 
, the only Hermite number with prime absolute value is 
.
The Hermite numbers 
are related to the Hermite polynomials 
by
 |
(3)
|
where 
, and
 |
(4)
|
where 
.
