cp's OEIS Frontend

A159651 Numerator of Hermite(n, 13/19).

%I A159651 #20 Sep 08 2022 08:45:44
%S A159651 1,26,-46,-38740,-907604,88283416,5571819256,-237576457456,
%T A159651 -34336962413680,479480595510176,235588077247357216,
%U A159651 2663440108847816896,-1801791066668467770176,-69922612836437647611520,15093623018002859652972416,1099211969018786093034526976
%N A159651 Numerator of Hermite(n, 13/19).
%H A159651 Vincenzo Librandi, <a href="/A159651/b159651.txt">Table of n, a(n) for n = 0..200</a>
%H A159651 DLMF <a href="https://dlmf.nist.gov/18.9">Digital library of mathematical functions</a>, Table 18.9.1 for H_n(x)
%F A159651 D-finite with recurrence a(n) -26*a(n-1) +722*(n-1)*a(n-2)=0. [DLMF] - _R. J. Mathar_, Feb 16 2014
%F A159651 From _G. C. Greubel_, Jul 11 2018: (Start)
%F A159651 a(n) = 19^n * Hermite(n, 13/19).
%F A159651 E.g.f.: exp(26*x - 361*x^2).
%F A159651 a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(26/19)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e A159651 Numerator of 1, 26/19, -46/361, -38740/6859, -907604/130321, 88283416/2476099,..
%p A159651 A159651 := proc(n)
%p A159651         orthopoly[H](n,13/19) ;
%p A159651         numer(%) ;
%p A159651 end proc: # _R. J. Mathar_, Feb 16 2014
%t A159651 Numerator[Table[HermiteH[n, 13/19], {n, 0, 30}]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 16 2011 *)
%t A159651 Table[19^n*HermiteH[n, 13/19], {n,0,50}] (* _G. C. Greubel_, Jul 11 2018 *)
%o A159651 (PARI) a(n)=numerator(polhermite(n,13/19)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o A159651 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(26/19)^(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 A159651 Cf. A001029 (denominators).
%K A159651 sign,frac
%O A159651 0,2
%A A159651 _N. J. A. Sloane_, Nov 12 2009