cp's OEIS Frontend

A159655 Numerator of Hermite(n, 17/19).

%I A159655 #19 Sep 08 2022 08:45:44
%S A159655 1,34,434,-34340,-2107604,27515384,8543973496,171298455376,
%T A159655 -37357094566000,-2259561093495776,165921323311011616,
%U A159655 21955356087613897664,-571265042757181733696,-209644216596830988306560,-1766009672973345849952384,2059039412479673870904327424
%N A159655 Numerator of Hermite(n, 17/19).
%H A159655 Vincenzo Librandi, <a href="/A159655/b159655.txt">Table of n, a(n) for n = 0..200</a>
%H A159655 DLMF <a href="https://dlmf.nist.gov/18.9">Digital library of mathematical functions</a>, Table 18.9.1 for H_n(x)
%F A159655 D-finite with recurrence a(n) -34*a(n-1) +722*(n-1)*a(n-2)=0. [DLMF] - _R. J. Mathar_, Feb 16 2014
%F A159655 From _G. C. Greubel_, Jul 11 2018: (Start)
%F A159655 a(n) = 19^n * Hermite(n, 17/19).
%F A159655 E.g.f.: exp(34*x - 361*x^2).
%F A159655 a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(34/19)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e A159655 Numerator of 1, 34/19, 434/361, -34340/6859, -2107604/130321, 27515384/2476099,..
%p A159655 A159655 := proc(n)
%p A159655         orthopoly[H](n,17/19) ;
%p A159655         numer(%) ;
%p A159655 end proc: # _R. J. Mathar_, Feb 16 2014
%t A159655 Numerator[Table[HermiteH[n, 17/19], {n, 0, 30}]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 16 2011 *)
%t A159655 Table[19^n*HermiteH[n, 17/19], {n,0,50}] (* _G. C. Greubel_, Jul 11 2018 *)
%o A159655 (PARI) a(n)=numerator(polhermite(n,17/19)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o A159655 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(34/19)^(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 A159655 Cf. A001029 (denominators).
%K A159655 sign,frac
%O A159655 0,2
%A A159655 _N. J. A. Sloane_, Nov 12 2009