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%I #18 Sep 08 2022 08:45:43
%S 1,9,-47,-2727,-6495,1337769,16196721,-881636103,-22446986943,
%T 700772486985,32165881341201,-607495851269991,-50757023589840927,
%U 476300415242137833,88746390990674543025,-54812825197840109511,-170886386128875683593599
%N Numerator of Hermite(n, 9/16).
%H Vincenzo Librandi, <a href="/A159525/b159525.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) -9*a(n-1) +128*(n-1)*a(n-2)=0. [DLMF] - _R. J. Mathar_, Feb 16 2014
%F From _G. C. Greubel_, Jun 09 2018: (Start)
%F a(n) = 16^n * Hermite(n,9/16).
%F E.g.f.: exp(18*x-252*x^2).
%F a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*(9/8)^(n-2k)/(k!*(n-2k)!). (End)
%e Numerator of 1, 9/8, -47/64, -2727/512, -6495/4096, 1337769/32768...
%p A159525 := proc(n)
%p orthopoly[H](n,9/16) ;
%p numer(%) ;
%p end proc: # _R. J. Mathar_, Feb 16 2014
%t Numerator[Table[HermiteH[n,9/16],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 29 2011 *)
%o (PARI) a(n)=numerator(polhermite(n,9/16)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(9/8)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jun 09 2018
%Y Cf. A001018 (denominators).
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009
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