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%I #13 Sep 08 2022 08:45:44
%S 1,28,-674,-100520,133516,589971088,15545858824,-4725783030752,
%T -290982960018800,46974010390164928,5133550692291311584,
%U -541141652104447925888,-97483852261892597109056,6738266481886428192282880,2036380397264732274988968064,-80522844304853268561187040768
%N Numerator of Hermite(n, 14/27).
%H G. C. Greubel, <a href="/A160141/b160141.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, 14/27).
%F E.g.f.: exp(28*x - 729*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(28/27)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerators of 1, 28/27, -674/729, -100520/19683, 133516/531441, ...
%t Table[27^n*HermiteH[n, 14/27], {n, 0, 30}] (* _G. C. Greubel_, Sep 24 2018 *)
%o (PARI) a(n)=numerator(polhermite(n, 14/27)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(28*x - 729*x^2))) \\ _G. C. Greubel_, Sep 24 2018
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(28/27)^(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