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

			(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 .

REFERENCES:

Sloane, N. J. A. Sequence A067994 in "The On-Line Encyclopedia of Integer Sequences."