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Numerator of Hermite(n, 5/18).
5

%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