OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..450
DLMF, Digital library of mathematical functions, Table 18.9.1 for H_n(x).
FORMULA
From G. C. Greubel, Jun 02 2018: (Start)
a(n) = 3^n * Hermite(n, 1/6).
E.g.f.: exp(x - 9*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(1/3)^(n-2*k)/(k!*(n-2*k)!)). (End)
D-finite with recurrence a(n) -a(n-1) +18*(n-1)*a(n-2)=0. - [DLMF] Georg Fischer, Feb 06 2021
MATHEMATICA
Numerator[Table[HermiteH[n, 1/6], {n, 0, 50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 01 2011 *)
Table[3^n*HermiteH[n, 1/6], {n, 0, 50}] (* G. C. Greubel, Jul 10 2018 *)
PROG
(PARI) a(n)=numerator(polhermite(n, 1/6)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(1/3)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 10 2018
(SageMath) [3^n*hermite(n, 1/6) for n in range(31)] # G. C. Greubel, Jul 12 2024
CROSSREFS
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, Nov 12 2009
STATUS
approved