%I #13 Sep 08 2022 08:45:44
%S 1,32,-434,-107200,-1532084,576163712,29606131144,-4092883955968,
%T -433132461046640,33879159708918272,6767697264539394784,
%U -277391836090767772672,-117416867483587382271296,1095907804769276717987840,2260588356036532098545755264
%N Numerator of Hermite(n, 16/27).
%H G. C. Greubel, <a href="/A160142/b160142.txt">Table of n, a(n) for n = 0..375</a>
%F From _G. C. Greubel_, Sep 24 2018: (Start)
%F a(n) = 27^n * Hermite(n, 16/27).
%F E.g.f.: exp(32*x - 729*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(32/27)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerators of 1, 32/27, -434/729, -107200/19683, -1532084/531441, ...
%t Table[27^n*HermiteH[n, 16/27], {n, 0, 30}] (* _G. C. Greubel_, Sep 24 2018 *)
%o (PARI) a(n)=numerator(polhermite(n, 16/27)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(32*x - 729*x^2))) \\ _G. C. Greubel_, Sep 24 2018
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(32/27)^(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