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Numerator of Hermite(n, 2/9).
5

%I #12 Sep 08 2022 08:45:43

%S 1,4,-146,-1880,63436,1471984,-45495224,-1612749344,45140586640,

%T 2270685496384,-56732233335584,-3905439437484416,85475082054073024,

%U 7934074594685996800,-148274224427133801344,-18587578078456375947776,285956053044109633474816

%N Numerator of Hermite(n, 2/9).

%H G. C. Greubel, <a href="/A159197/b159197.txt">Table of n, a(n) for n = 0..450</a>

%F From _G. C. Greubel_, Jun 10 2018: (Start)

%F a(n) = 9^n * Hermite(n,2/9).

%F E.g.f.: exp(4*x-81*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(4/9)^(n-2*k)/(k!*(n-2*k)!)). (End)

%t Numerator[Table[HermiteH[n,2/9],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 01 2011*)

%o (PARI) a(n)=numerator(polhermite(n,2/9)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(4/9)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jun 10 2018

%Y Cf. A159030.

%K sign,frac

%O 0,2

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