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A159850 Numerator of Hermite(n, 17/22). 2

%I

%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 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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Last modified December 10 04:15 EST 2019. Contains 329885 sequences. (Running on oeis4.)