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%I #21 Sep 08 2022 08:45:44
%S 1,3,-191,-1773,109281,1746243,-104042271,-2407618413,138436324161,
%T 4267498433283,-236382888189951,-9244145531135853,492309917424484641,
%U 23662879026999501123,-1209017148222661563231,-69883112720266587834093,3417402106507184926190721
%N Numerator of Hermite(n, 3/20).
%H Vincenzo Librandi, <a href="/A159658/b159658.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) -3*a(n-1) +200*(n-1)*a(n-2)=0. [DLMF] - _R. J. Mathar_, Feb 16 2014
%F From _G. C. Greubel_, Jul 11 2018: (Start)
%F a(n) = 10^n * Hermite(n, 3/20).
%F E.g.f.: exp(3*x - 100*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(3/10)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerator of 1, 3/10, -191/100, -1773/1000, 109281/10000, 1746243/100000..
%p A159658 := proc(n)
%p orthopoly[H](n,3/20) ;
%p numer(%) ;
%p end proc: # _R. J. Mathar_, Feb 16 2014
%t Numerator[Table[HermiteH[n, 3/20], {n, 0, 30}]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 16 2011 *)
%t Table[10^n*HermiteH[n, 3/20], {n,0,50}] (* _G. C. Greubel_, Jul 11 2018 *)
%o (PARI) a(n)=numerator(polhermite(n,3/20)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(3/10)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 11 2018
%Y Cf. A011557 (denominators).
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009
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