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%I #13 Sep 08 2022 08:45:44
%S 1,4,-706,-8600,1494796,30815984,-5272949624,-154586641184,
%T 26031140834960,997017002818624,-165162285134295584,
%U -7859111900887647616,1280282420933024937664,73212475193022678695680,-11723880902105281350131584,-786927222859494361656459776
%N Numerator of Hermite(n, 2/19).
%H G. C. Greubel, <a href="/A159618/b159618.txt">Table of n, a(n) for n = 0..397</a>
%F From _G. C. Greubel_, Jun 09 2018: (Start)
%F a(n) = 19^n * Hermite(n,2/19).
%F E.g.f.: exp(4*x-361*x^2).
%F a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*(4/19)^(n-2k)/(k!*(n-2k)!). (End)
%t Numerator[Table[HermiteH[n,2/19],{n,0,30}]] (* _Vladimir Joseph Stephan Orlovsky_, May 20 2011 *)
%o (PARI) a(n)=numerator(polhermite(n,2/19)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(4/19)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jun 09 2018
%Y Cf. A159564.
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009
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