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%I #12 Sep 08 2022 08:45:43
%S 1,3,-23,-261,1425,37683,-114951,-7579989,3009057,1949504355,
%T 4981904649,-608895679653,-3580317475407,223074988560531,
%U 2158637035450905,-93461683768765173,-1316530828322729919,43902789604639578819,847901139421483812393
%N Numerator of Hermite(n, 3/8).
%H G. C. Greubel, <a href="/A159017/b159017.txt">Table of n, a(n) for n = 0..450</a>
%F From _G. C. Greubel_, Jul 09 2018: (Start)
%F a(n) = 4^n * Hermite(n, 3/8).
%F E.g.f.: exp(3*x - 16*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(3/4)^(n-2*k)/(k!*(n-2*k)!)). (End)
%t Numerator[Table[HermiteH[n,3/8],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 01 2011*)
%t Table[4^n*HermiteH[n, 3/8], {n,0,30}] (* _G. C. Greubel_, Jul 09 2018 *)
%o (PARI) a(n)=numerator(polhermite(n,3/8)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(3/4)^(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
%Y Cf. A159014.
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009