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%I #13 Sep 08 2022 08:45:45
%S 1,27,337,-12069,-722175,-574533,1399950609,39149968059,
%T -2784415333503,-197953513837605,4478672422983249,896901929663959323,
%U 4904316613023132033,-4086610128587640090501,-135330870931832163283695,18773382870529500408009723
%N Numerator of Hermite(n, 27/28).
%H G. C. Greubel, <a href="/A160223/b160223.txt">Table of n, a(n) for n = 0..417</a>
%F From _G. C. Greubel_, Sep 26 2018: (Start)
%F a(n) = 14^n * Hermite(n, 27/28).
%F E.g.f.: exp(27*x - 196*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(27/14)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerators of 1, 27/14, 337/196, -12069/2744, -722175/38416
%t Table[14^n*HermiteH[n, 27/28], {n, 0, 30}] (* _G. C. Greubel_, Sep 26 2018 *)
%o (PARI) a(n)=numerator(polhermite(n, 27/28)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(27*x - 196*x^2))) \\ _G. C. Greubel_, Sep 26 2018
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(27/14)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Sep 26 2018
%Y Cf. A001023 (denominators).
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009
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