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) +98*(n-1)*a(n-2)=0. [DLMF] - R. J. Mathar, Feb 16 2014
From G. C. Greubel, Jul 09 2018: (Start)
a(n) = 7^n * Hermite(n, 4/7).
E.g.f.: exp(8*x - 49*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(8/7)^(n-2*k)/(k!*(n-2*k)!)). (End)
EXAMPLE
Numerator of 1, 8/7, -34/49, -1840/343, -4724/2401, 683488/16807, 7782664/117649...
MAPLE
MATHEMATICA
Numerator[Table[HermiteH[n, 4/7], {n, 0, 50}]] (* Vladimir Joseph Stephan Orlovsky, Mar 23 2011*)
Table[7^n*HermiteH[n, 4/7], {n, 0, 30}] (* G. C. Greubel, Jul 09 2018 *)
PROG
(PARI) a(n)=numerator(polhermite(n, 4/7)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(8/7)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 09 2018
CROSSREFS
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, Nov 12 2009
STATUS
approved