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%I #12 Sep 08 2022 08:45:43
%S 1,4,-434,-5336,564556,11863024,-1222798904,-36921360416,
%T 3704131105936,147733421921344,-14410797291355424,-722443587811469696,
%U 68443672240963470016,4174970063145790238464,-383695602357053138639744,-27837093807246691056882176,2478596940681121921590743296
%N Numerator of Hermite(n, 2/15).
%H G. C. Greubel, <a href="/A159514/b159514.txt">Table of n, a(n) for n = 0..412</a>
%F From _G. C. Greubel_, Jun 11 2018: (Start)
%F a(n) = 15^n * Hermite(n,2/15).
%F E.g.f.: exp(4*x-225*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(4/15)^(n-2*k)/(k!*(n-2*k)!)). (End)
%t Numerator[Table[HermiteH[n,2/15],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 28 2011 *)
%o (PARI) a(n)=numerator(polhermite(n,2/15)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(4/15)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jun 11 2018
%Y Cf. A159513.
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009