Hermite Number
المؤلف:
Sloane, N. J. A.
المصدر:
Sequence A067994 in "The On-Line Encyclopedia of Integer Sequences."
الجزء والصفحة:
...
4-1-2021
1976
Hermite Number
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
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 
.
REFERENCES:
Sloane, N. J. A. Sequence A067994 in "The On-Line Encyclopedia of Integer Sequences."
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