%I #15 Sep 08 2022 08:45:43

%S 1,1,-161,-485,77761,392041,-62594369,-443658221,70538356225,

%T 645519410641,-102199403965409,-1147940849203829,180971397017155009,

%U 2412568407869398585,-378713193710259050369,-5850418342758055041149,914422642373171437355521

%N Numerator of Hermite(n, 1/18).

%H G. C. Greubel, <a href="/A159545/b159545.txt">Table of n, a(n) for n = 0..450</a>

%F From _G. C. Greubel_, Jun 09 2018: (Start)

%F a(n) = 9^n * Hermite(n,1/18).

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

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

%t Numerator[Table[HermiteH[n,1/18],{n,0,30}]] (* _Vladimir Joseph Stephan Orlovsky_, May 20 2011 *)

%o (PARI) a(n)=numerator(polhermite(n,1/18)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(1/9)^(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. A159542, A159543, A159544.

%K sign,frac

%O 0,3

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