%I #13 Sep 08 2022 08:45:44
%S 1,40,142,-110960,-5059508,444738400,54673349320,-1703637550400,
%T -626141705175920,-5174439819171200,8009253862551574240,
%U 395813487065579065600,-112619873964978985037120,-11429947728298530733222400,1677399182000270453064676480
%N Numerator of Hermite(n, 20/27).
%H G. C. Greubel, <a href="/A160148/b160148.txt">Table of n, a(n) for n = 0..376</a>
%F From _G. C. Greubel_, Sep 24 2018: (Start)
%F a(n) = 27^n * Hermite(n, 20/27).
%F E.g.f.: exp(40*x - 729*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(40/27)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerators of 1, 40/27, 142/729, -110960/19683, -5059508/531441, ...
%t Table[27^n*HermiteH[n, 20/27], {n, 0, 30}] (* _G. C. Greubel_, Sep 24 2018 *)
%o (PARI) a(n)=numerator(polhermite(n, 20/27)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(40*x - 729*x^2))) \\ _G. C. Greubel_, Sep 24 2018
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(40/27)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Sep 24 2018
%Y Cf. A009971 (denominators).
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009
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