%I #20 Sep 08 2022 08:45:44

%S 1,9,-161,-5805,64641,6201009,-22406529,-9205523829,-44893054335,

%T 17417856643929,254537782136991,-39860373039075261,

%U -1036322933400347391,106427616904871431425,4218120500621335774911,-322613681568112387693701,-18215300551368460352170239

%N Numerator of Hermite(n, 9/22).

%H G. C. Greubel, <a href="/A159831/b159831.txt">Table of n, a(n) for n = 0..435</a>

%F From _G. C. Greubel_, Jul 11 2018: (Start)

%F a(n) = 11^n * Hermite(n, 9/22).

%F E.g.f.: exp(9*x - 121*x^2).

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

%e Numerators of 1, 9/11, -161/121, -5805/1331, 64641/14641, ...

%t Numerator[Table[HermiteH[n, 9/22], {n, 0, 30}]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 17 2011 *)

%t Table[11^n*HermiteH[n, 9/22], {n,0,30}] (* _G. C. Greubel_, Jul 11 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 9/22)) \\ _Charles R Greathouse IV_, Jan 29 2016

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

%Y Cf. A001020 (denominators).

%K sign,frac

%O 0,2

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