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%I #21 Sep 08 2022 08:45:44
%S 1,19,119,-6935,-218159,2568059,312765511,2213723041,-487764037855,
%T -13553284526621,804837668442391,48090864254828249,
%U -1228751452551908111,-163002147394507489205,768611269232660622311,566854889488011925250449,7980183992957668520769601
%N Numerator of Hermite(n, 19/22).
%H G. C. Greubel, <a href="/A159851/b159851.txt">Table of n, a(n) for n = 0..434</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)
%H Simon Plouffe, <a href="http://vixra.org/abs/1409.0048"> Conjectures of the OEIS, as of June 20, 2018.</a>
%F E.g.f.: exp(-x*(121*x-19)). - _Simon Plouffe_, Jun 22 2018
%F From _G. C. Greubel_, Jul 14 2018: (Start)
%F a(n) = 11^n * Hermite(n, 19/22).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(19/11)^(n-2*k)/(k!*(n-2*k)!)). (End)
%F D-finite with recurrence a(n) -19*a(n-1) +242*(n-1)*a(n-2)=0. [DLMF] - _R. J. Mathar_, Feb 06 2021
%e Numerators of 1, 19/11, 119/121, -6935/1331, -218159/14641, ...
%t Numerator[Table[HermiteH[n,19/22],{n,0,30}]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 22 2011 *)
%t Table[11^n*HermiteH[n, 19/22], {n,0,30}] (* _G. C. Greubel_, Jul 14 2018 *)
%o (PARI) a(n)=numerator(polhermite(n, 19/22)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(19*x - 121*x^2))) \\ _G. C. Greubel_, Jul 14 2018
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(19/11)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 14 2018
%Y Cf. A001020 (denominators).
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009