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%I #16 Sep 08 2022 08:45:43
%S 1,4,-226,-2840,152716,3359984,-171346424,-5564082464,268004512400,
%T 11844081699904,-536337501207584,-30808027718598016,
%U 1304498317340196544,94684505764169424640,-3725213683295580628864,-335691960262188333195776,12179757829314204349993216
%N Numerator of Hermite(n, 2/11).
%C Denominator is 11^n. - _Robert Israel_, May 21 2014
%H G. C. Greubel, <a href="/A159281/b159281.txt">Table of n, a(n) for n = 0..434</a> (terms 0..82 from Robert Israel)
%F a(n) = 4*a(n-1) - 242*(n-1)*a(n-2) for n >= 2.
%F E.g.f.: exp(-11*x^2 + 4*x). - _Robert Israel_, May 21 2014
%F From _G. C. Greubel_, Jun 27 2018: (Start)
%F a(n) = 11^n * Hermite(n, 2/11).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(4/11)^(n-2*k)/(k!*(n-2*k)!)). (End)
%p N:= 30; # to get a(n) for n <= N
%p A159281[0]:= 1:
%p A159281[1]:= 4:
%p for n from 2 to N do
%p A159281[n]:= 4*A159281[n-1] - 242*(n-1)*A159281[n-2]
%p od:
%p seq(A159281[n],n=0..N); # _Robert Israel_, May 21 2014
%t Numerator[Table[HermiteH[n,2/11],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 12 2011 *)
%o (PARI) a(n)=numerator(polhermite(n,2/11)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(4/11)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jun 27 2018
%Y Cf. A159280.
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009
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