%I #28 Sep 08 2022 08:45:44
%S 1,17,47,-7429,-160415,4464217,269993839,-1892147821,-489536076223,
%T -4658915114335,987008017069999,28053710866880683,
%U -2150502256703365727,-118026514721378720791,4759029349325350323695,480777330814562061542723,-9102061914203466628786559
%N Numerator of Hermite(n, 17/22).
%H Robert Israel, <a href="/A159850/b159850.txt">Table of n, a(n) for n = 0..435</a>
%H Simon Plouffe, <a href="http://vixra.org/abs/1409.0048">Conjectures of the OEIS, as of June 20, 2018.</a>
%F D-finite with recurrence a(n) = 17*a(n-1) + 242*(1-n)*a(n-2). - _Robert Israel_, Dec 07 2017
%F E.g.f.: exp(17*x - 121*x^2). - _Simon Plouffe_, Jun 23 2018
%F From _G. C. Greubel_, Jun 02 2018: (Start)
%F a(n) = 11^n * Hermite(n, 17/22).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(17/11)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerators of 1, 17/11, 47/121, -7429/1331, -160415/14641, ...
%p f:= gfun:-rectoproc({a(n) = 17*a(n-1)+242*(1-n)*a(n-2), a(0)=1,a(1)=17},a(n),remember):
%p map(f, [$0..40]); # _Robert Israel_, Dec 07 2017
%t Numerator[Table[HermiteH[n,17/22],{n,0,30}]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 22 2011 *)
%t Table[11^n*HermiteH[n, 17/22], {n,0,30}] (* _G. C. Greubel_, Jul 09 2018 *)
%o (PARI) a(n)=numerator(polhermite(n, 17/22)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(17/11)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 09 2018
%Y Cf. A001020 (denominators).
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009
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