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%I #23 Mar 18 2024 12:03:04
%S 1,38,562,-45676,-3222740,38680808,15682154104,391223020016,
%T -81955144677488,-5874765126977440,427318863624757024,
%U 68053545237681787712,-1559812895855484713792,-779551612838132460267904,-11738146623970045761841280,9179853743614397880438109952
%N Numerator of Hermite(n, 19/21).
%H G. C. Greubel, <a href="/A159784/b159784.txt">Table of n, a(n) for n = 0..390</a>
%F From _G. C. Greubel_, Jul 11 2018: (Start)
%F a(n) = 21^n * Hermite(n, 19/21).
%F E.g.f.: exp(38*x - 441*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(38/21)^(n-2*k)/(k!*(n-2*k)!)). (End)
%t Numerator[Table[HermiteH[n, 19/21], {n, 0, 30}]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 17 2011 *)
%t Table[21^n*HermiteH[n, 19/21], {n,0,50}] (* _G. C. Greubel_, Jul 11 2018 *)
%o (PARI) a(n)=numerator(polhermite(n, 19/21)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(38/21)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, May 21 2018
%Y Cf. A009965 (denominators).
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009
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