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%I #13 Sep 08 2022 08:45:43
%S 1,4,-2,-152,-500,8944,80776,-642848,-12749168,41573440,2231658976,
%T 1443416704,-436094810432,-2056157249792,93821556641920,
%U 893437853515264,-21758068879257344,-344342377329425408,5280599567735045632,132689328525674014720,-1275207738062689547264
%N Numerator of Hermite(n, 2/3).
%H G. C. Greubel, <a href="/A158903/b158903.txt">Table of n, a(n) for n = 0..450</a>
%F From _G. C. Greubel_, Jul 13 2018: (Start)
%F a(n) = 3^n * Hermite(n, 2/3).
%F E.g.f.: exp(4*x - 9*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(4/3)^(n-2*k)/(k!*(n-2*k)!)). (End)
%t Numerator[Table[HermiteH[n,2/3],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Mar 23 2011*)
%t Table[3^n*HermiteH[n, 2/3], {n,0,30}] (* _G. C. Greubel_, Jul 13 2018 *)
%o (PARI) a(n)=3^n*polhermite(n,2/3) \\ _Charles R Greathouse IV_, Jun 19 2012
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(4*x - 9*x^2))) \\ _G. C. Greubel_, Jul 13 2018
%o (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
%Y The denominators are A000244.
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009
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