%I #12 Sep 08 2022 08:45:44
%S 1,22,-574,-59180,519916,261887912,3011178424,-1596218540048,
%T -57417595289200,12247206626603872,816168888129047584,
%U -111619730570629918912,-11954207592599713998656,1154131532287523742536320,189809064938941988673313664,-12919196827586077923635071232
%N Numerator of Hermite(n, 11/23).
%H G. C. Greubel, <a href="/A159875/b159875.txt">Table of n, a(n) for n = 0..385</a>
%F From _G. C. Greubel_, Jul 15 2018: (Start)
%F a(n) = 23^n * Hermite(n, 11/23).
%F E.g.f.: exp(22*x - 529*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(22/23)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerators of 1, 22/23, -574/529, -59180/12167, 519916/279841,..
%t Numerator[HermiteH[Range[0,20],11/23]] (* _Harvey P. Dale_, Nov 20 2012 *)
%t Table[23^n*HermiteH[n,11/23], {n,0,30}] (* _G. C. Greubel_, Jul 15 2018 *)
%o (PARI) a(n)=numerator(polhermite(n, 11/23)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(22*x - 529*x^2))) \\ _G. C. Greubel_, Jul 15 2018
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(22/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 15 2018
%Y Cf. A009967 (denominators)
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009