%I #15 Sep 08 2022 08:45:43
%S 1,4,-34,-536,2956,119024,-262904,-36758816,-55018864,14483450944,
%T 82692292576,-6910956301696,-73124586123584,3854075436523264,
%U 62947282726422656,-2446063674660594176,-56994716743459368704,1728872072754637865984
%N Numerator of Hermite(n, 2/5).
%H G. C. Greubel, <a href="/A158961/b158961.txt">Table of n, a(n) for n = 0..450</a>
%F From _G. C. Greubel_, Jul 09 2018: (Start)
%F a(n) = 5^n * Hermite(n, 2/5).
%F E.g.f.: exp(4*x-25*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(4/5)^(n-2*k)/(k!*(n-2*k)!)). (End)
%t Numerator[Table[HermiteH[n,2/5],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 01 2011 *)
%t Table[5^n*HermiteH[n, 2/5], {n,0,30}] (* _G. C. Greubel_, Jul 09 2018 *)
%o (PARI) a(n)=numerator(polhermite(n,2/5)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(4/5)^(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. A158954, A158960.
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009
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