OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
DLMF Digital library of mathematical functions, Table 18.9.1 for H_n(x)
FORMULA
D-finite with recurrence a(n) - 8*a(n-1) + 882*(n-1)*a(n-2) = 0. [DLMF] - R. J. Mathar, Feb 17 2014
From G. C. Greubel, May 22 2018: (Start)
a(n) = 21^n * Hermite(n,4/21).
E.g.f.: exp(8*x-441*x^2).
a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*(8/21)^(n-2k)/(k!*(n-2k)!). (End)
EXAMPLE
Numerator of 1, 8/21, -818/441, -20656/9261, 1999180/194481, 88867808/4084101, ...
MAPLE
MATHEMATICA
Numerator[Table[HermiteH[n, 4/21], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 17 2011 *)
PROG
(PARI) a(n)=numerator(polhermite(n, 4/21)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(8/21)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, May 22 2018
CROSSREFS
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, Nov 12 2009
STATUS
approved