OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..450
FORMULA
From G. C. Greubel, Jul 13 2018: (Start)
a(n) = 3^n * Hermite(n, 2/3).
E.g.f.: exp(4*x - 9*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(4/3)^(n-2*k)/(k!*(n-2*k)!)). (End)
MATHEMATICA
Numerator[Table[HermiteH[n, 2/3], {n, 0, 50}]] (* Vladimir Joseph Stephan Orlovsky, Mar 23 2011*)
Table[3^n*HermiteH[n, 2/3], {n, 0, 30}] (* G. C. Greubel, Jul 13 2018 *)
PROG
(PARI) a(n)=3^n*polhermite(n, 2/3) \\ Charles R Greathouse IV, Jun 19 2012
(PARI) x='x+O('x^30); Vec(serlaplace(exp(4*x - 9*x^2))) \\ G. C. Greubel, Jul 13 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(4/3)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 13 2018
CROSSREFS
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, Nov 12 2009
STATUS
approved