%I #11 Sep 08 2022 08:45:44

%S 1,11,-41,-4015,-24239,2335091,45319591,-1771192951,-70875538655,

%T 1515835139291,120010721891191,-1135534984848319,-226349991243433871,

%U -282369893132640445,473587012734212687431,5849872057701168091001,-1086467848309423981456319

%N Numerator of Hermite(n, 11/18).

%H G. C. Greubel, <a href="/A159561/b159561.txt">Table of n, a(n) for n = 0..450</a>

%F From _G. C. Greubel_, Jun 02 2018: (Start)

%F a(n) = 9^n * Hermite(n, 11/18).

%F E.g.f.: exp(11*x - 81*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(11/9)^(n-2*k)/(k!*(n-2*k)!)). (End)

%t Numerator[Table[HermiteH[n,11/18],{n,0,30}]] (* _Vladimir Joseph Stephan Orlovsky_, May 20 2011 *)

%t Table[9^n*HermiteH[n, 11/18], {n,0,30}] (* _G. C. Greubel_, Jul 14 2018 *)

%o (PARI) a(n)=numerator(polhermite(n,11/18)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(11*x - 81*x^2))) \\ _G. C. Greubel_, Jul 14 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(11/9)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 14 2018

%Y Cf. A159545, A159546.

%K sign,frac

%O 0,2

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