cp's OEIS Frontend

A159648 Numerator of Hermite(n, 10/19).

%I A159648 #23 Sep 08 2022 08:45:44
%S A159648 1,20,-322,-35320,-8948,101825200,2068806280,-399730640800,
%T A159648 -18450359755120,1939836986158400,158687177411937760,
%U A159648 -10831879491824892800,-1476931152842107545920,64308780860328720300800,15148651417782595832021120,-347060128580550788160064000
%N A159648 Numerator of Hermite(n, 10/19).
%H A159648 Vincenzo Librandi, <a href="/A159648/b159648.txt">Table of n, a(n) for n = 0..200</a>
%H A159648 DLMF <a href="https://dlmf.nist.gov/18.9">Digital library of mathematical functions</a>, Table 18.9.1 for H_n(x)
%F A159648 D-finite with recurrence a(n) - 20*a(n-1) + 722*(n-1)*a(n-2) = 0. [DLMF] - _R. J. Mathar_, Feb 16 2014
%F A159648 From _G. C. Greubel_, Jul 10 2018: (Start)
%F A159648 a(n) = 19^n * Hermite(n, 10/19).
%F A159648 E.g.f.: exp(20*x - 361*x^2).
%F A159648 a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(20/19)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e A159648 Numerator of 1, 20/19, -322/361, -35320/6859, -8948/130321, 101825200/2476099, ...
%p A159648 A159648 := proc(n)
%p A159648         orthopoly[H](n,10/19) ;
%p A159648         numer(%) ;
%p A159648 end proc: # _R. J. Mathar_, Feb 16 2014
%t A159648 Numerator[Table[HermiteH[n,10/19],{n,0,30}]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 16 2011 *)
%t A159648 Table[19^n*HermiteH[n, 10/19], {n,0,50}] (* _G. C. Greubel_, Jul 10 2018 *)
%o A159648 (PARI) a(n)=numerator(polhermite(n,10/19)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o A159648 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(20/19)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 10 2018
%Y A159648 Cf. A001029 (denominators).
%K A159648 sign,frac
%O A159648 0,2
%A A159648 _N. J. A. Sloane_, Nov 12 2009