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%I #21 Sep 08 2022 08:45:44
%S 1,16,-626,-38240,1044556,151623616,-2180514104,-837280401536,
%T 66007653520,5908906635694336,94018537417467616,-50612259928144561664,
%U -1721964008874583797056,508128734937488699898880,27874099084755797015426176,-5828388033652017714104551424
%N Numerator of Hermite(n, 8/21).
%H Vincenzo Librandi, <a href="/A159745/b159745.txt">Table of n, a(n) for n = 0..200</a>
%H DLMF <a href="https://dlmf.nist.gov/18.9">Digital library of mathematical functions</a>, Table 18.9.1 for H_n(x)
%F D-finite with recurrence a(n) -16*a(n-1) +882*(n-1)*a(n-2)=0. [DLMF] - _R. J. Mathar_, Feb 17 2014
%F From _G. C. Greubel_, May 22 2018: (Start)
%F a(n) = 21^n * Hermite(n,8/21).
%F E.g.f.: exp(16*x-441*x^2).
%F a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*(16/21)^(n-2k)/(k!*(n-2k)!). (End)
%t Numerator[Table[HermiteH[n, 8/21], {n, 0, 30}]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 17 2011 *)
%o (PARI) a(n)=numerator(polhermite(n,8/21)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(16/21)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, May 22 2018
%Y Cf. A009965 (denominators).
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009
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