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%I #17 Sep 08 2022 08:45:44
%S 1,7,-151,-3857,63601,3530807,-38885351,-4509165857,22875330401,
%T 7374792684007,10447954066249,-14676449689550257,-125720646772599599,
%U 34343434727512419607,567277724701345894649,-92190673164125353637057,-2347167886252915159406399
%N Numerator of Hermite(n, 7/20).
%H G. C. Greubel, <a href="/A159659/b159659.txt">Table of n, a(n) for n = 0..442</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) -7*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, 7/20).
%F E.g.f.: exp(7*x - 100*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(7/10)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerator of 1, 7/10, -151/100, -3857/1000, 63601/10000, 3530807/100000,...
%p A159659 := proc(n)
%p orthopoly[H](n,7/20) ;
%p numer(%) ;
%p end proc: # _R. J. Mathar_, Feb 16 2014
%t Numerator[Table[HermiteH[n, 7/20], {n, 0, 30}]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 16 2011 *)
%t Table[10^n*HermiteH[n, 7/20], {n,0,50}] (* _G. C. Greubel_, Jul 11 2018 *)
%o (PARI) a(n)=numerator(polhermite(n,7/20)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(7/10)^(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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