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%I #20 Sep 08 2022 08:45:44
%S 1,36,574,-31320,-2370804,5103216,8742318216,292616324064,
%T -33649488597360,-2901533477298624,114199171722894816,
%U 25060241888120278656,-4801113850900597056,-217294775817306515769600,-7777548674818481563737984,1916423841667868925104549376
%N Numerator of Hermite(n, 18/19).
%H Vincenzo Librandi, <a href="/A159656/b159656.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) -36*a(n-1) +722*(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) = 19^n * Hermite(n, 18/19).
%F E.g.f.: exp(36*x - 361*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(36/19)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerator of 1, 36/19, 574/361, -31320/6859, -2370804/130321, 5103216/2476099,...
%p A159656 := proc(n)
%p orthopoly[H](n,18/19) ;
%p numer(%) ;
%p end proc: # _R. J. Mathar_, Feb 16 2014
%t Numerator[Table[HermiteH[n, 18/19], {n, 0, 30}]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 16 2011 *)
%t Table[19^n*HermiteH[n,18/19], {n,0,50}] (* _G. C. Greubel_, Jul 11 2018 *)
%o (PARI) a(n)=numerator(polhermite(n,18/19)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(36/19)^(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. A001029 (denominators).
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009
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