cp's OEIS Frontend

A158811 Numerator of Hermite(n, 1/3).

%I A158811 #25 Sep 08 2022 08:45:43
%S A158811 1,2,-14,-100,556,8312,-33416,-964528,2281360,143454752,-82670816,
%T A158811 -25987196992,-35605572416,5542023405440,19415750756224,
%U A158811 -1357758396658432,-7957769497497344,375118879242633728,3185315224719454720,-115167886425174418432,-1319713579704402351104
%N A158811 Numerator of Hermite(n, 1/3).
%H A158811 Vincenzo Librandi, <a href="/A158811/b158811.txt">Table of n, a(n) for n = 0..200</a>
%H A158811 DLMF <a href="https://dlmf.nist.gov/18.9">Digital library of mathematical functions</a>, Table 18.9.1 for H_n(x)
%F A158811 D-finite with recurrence a(n) -2*a(n-1) +18*(n-1)*a(n-2)=0. [DLMF] - _R. J. Mathar_, Feb 16 2014
%F A158811 From _G. C. Greubel_, Jun 09 2018: (Start)
%F A158811 a(n) = 3^n * Hermite(n,1/3).
%F A158811 E.g.f.: exp(2*x-9*x^2).
%F A158811 a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(2/3)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e A158811 Numerator of 1, 2/3, -14/9, -100/27, 556/81, 8312/243, -33416/729, -964528/2187, 2281360/6561, 143454752/19683, -82670816/59049,...
%p A158811 A158811 := proc(n)
%p A158811         orthopoly[H](n,1/3) ;
%p A158811         numer(%) ;
%p A158811 end proc: # _R. J. Mathar_, Feb 16 2014
%t A158811 Numerator[Table[HermiteH[n,1/3],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Mar 23 2011 *)
%o A158811 (PARI) a(n)=numerator(polhermite(n,1/3)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o A158811 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(2/3)^(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 A158811 Cf. A000244 (denominators).
%K A158811 sign,frac
%O A158811 0,2
%A A158811 _N. J. A. Sloane_, Nov 12 2009