%I #12 Sep 08 2022 08:45:43
%S 1,5,-137,-2305,55057,1768925,-35751545,-1898152825,31051487905,
%T 2615263500725,-32196751861865,-4397710630483825,35386058665424305,
%U 8726079758987677325,-30892640754445199705,-19945212097156278171625,-24656943452479555574975
%N Numerator of Hermite(n, 5/18).
%H G. C. Greubel, <a href="/A159546/b159546.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,5/18).
%F E.g.f.: exp(5*x-81*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(5/9)^(n-2*k)/(k!*(n-2*k)!)). (End)
%t Numerator[Table[HermiteH[n,5/18],{n,0,30}]] (* _Vladimir Joseph Stephan Orlovsky_, May 20 2011 *)
%o (PARI) a(n)=numerator(polhermite(n,5/18)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(5/9)^(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. A159545.
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009