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%I #23 Sep 08 2022 08:45:44
%S 1,19,161,-4541,-182879,158099,185882881,3342055939,-196736970559,
%T -9085291943021,181506000088801,21619197887729219,11451559671492961,
%U -51668495296791759341,-1011475465784925126079,125453752981103348759299,5418047703995739004663681
%N Numerator of Hermite(n, 19/20).
%H Vincenzo Librandi, <a href="/A159682/b159682.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) -19*a(n-1) +200*(n-1)*a(n-2)=0. [DLMF] - _R. J. Mathar_, Feb 17 2014
%F From _G. C. Greubel_, Jun 02 2018: (Start)
%F a(n) = 10^n * Hermite(n,19/20).
%F E.g.f.: exp(19*x-100*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(38/20)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerator of 1, 19/10, 161/100, -4541/1000, -182879/10000, 158099/100000,..
%p A159682 := proc(n)
%p orthopoly[H](n,19/20) ;
%p numer(%) ;
%p end proc: # _R. J. Mathar_, Feb 17 2014
%t Numerator[Table[HermiteH[n, 19/20], {n, 0, 30}]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 17 2011 *)
%o (PARI) a(n)=numerator(polhermite(n,19/20)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(38/20)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jun 02 2018
%Y Cf. A011557 (denominators).
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009
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