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A159307 Numerator of Hermite(n, 3/11). 1

%I

%S 1,6,-206,-4140,124716,4755816,-122371464,-7639673616,161459218320,

%T 15759163430496,-257103196917984,-39679794683308224,

%U 446329942095824064,117908103412902026880,-696705377356050344064,-403652886627048369133824,107123200040172534149376

%N Numerator of Hermite(n, 3/11).

%H G. C. Greubel, <a href="/A159307/b159307.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,6/11).

%F E.g.f.: exp(6*x - 121*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(6/11)^(n-2*k)/(k!*(n-2*k)!)). (End)

%F a(n) = 6*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,3/11],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 12 2011 *)

%o (PARI) a(n)=numerator(polhermite(n,3/11)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(6/11)^(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, 6]; [n le 2 select I[n] else 6*Self(n-1)-242*(n-2)*Self(n-2): n in [1..25]]; // _Vincenzo Librandi_, Jan 27 2018

%Y Cf. A159280.

%K sign,frac

%O 0,2

%A _N. J. A. Sloane_, Nov 12 2009

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Last modified September 23 03:34 EDT 2020. Contains 337291 sequences. (Running on oeis4.)