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%I #21 Sep 08 2022 08:45:43
%S 1,10,-142,-6260,40492,6464600,15650680,-9230092400,-118813175920,
%T 16681327127200,425588368425760,-36112927963566400,
%U -1494045516385037120,89931487642346454400,5599582070970791323520,-248692059422561874272000,-22813403511849591247097600
%N Numerator of Hermite(n, 5/11).
%H G. C. Greubel, <a href="/A159327/b159327.txt">Table of n, a(n) for n = 0..434</a>
%F From _G. C. Greubel_, Jun 26 2018: (Start)
%F a(n) = 11^n * Hermite(n,5/11).
%F E.g.f.: exp(10*x - 121*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(10/11)^(n-2*k)/(k!*(n-2*k)!)). (End)
%F a(n) = 10*a(n-1) - 242*(n-1)*a(n-2) for n>1. - _Vincenzo Librandi_, Jun 27 2018 [corrected by _Georg Fischer_, Dec 23 2019]
%t Numerator[Table[HermiteH[n,5/11],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 12 2011 *)
%t Table[11^n*HermiteH[n,5/11], {n,0,30}] (* _G. C. Greubel_, Jun 26 2018 *)
%t RecurrenceTable[{a[n] == 10*a[n-1] - 242*(n-1)*a[n-2], a[0]==1, a[1]==10}, a,{n,0,30}] (* _Georg Fischer_, Dec 23 2019 *)
%o (PARI) a(n)=numerator(polhermite(n,5/11)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(10/11)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jun 26 2018
%o (Magma) I:=[1, 10]; [n le 2 select I[n] else 10*Self(n-1)-242*(n-2)*Self(n-2): n in [1..25]]; // _Vincenzo Librandi_, Jun 27 2018
%Y Cf. A159280.
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009
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