A160150 - OEIS

%I #15 Sep 08 2022 08:45:44

%S 1,44,478,-107272,-6810740,325937744,63991555336,-35674949728,

%T -654667511547248,-28389257894451520,7341419739167121376,

%U 736937848624456502144,-85316424437286206533952,-16647387274774084049005312,884602468694263060488292480

%N Numerator of Hermite(n, 22/27).

%H G. C. Greubel, <a href="/A160150/b160150.txt">Table of n, a(n) for n = 0..375</a>

%F From _G. C. Greubel_, Sep 24 2018: (Start)

%F a(n) = 27^n * Hermite(n, 22/27).

%F E.g.f.: exp(44*x - 729*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(44/27)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 44/27, 478/729, -107272/19683, -6810740/531441, ...

%t Numerator[HermiteH[Range[0,20],22/27]] (* _Harvey P. Dale_, Jul 29 2013 *)

%t Table[27^n*HermiteH[n, 22/27], {n, 0, 30}] (* _G. C. Greubel_, Sep 24 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 22/27)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(44*x - 729*x^2))) \\ _G. C. Greubel_, Sep 24 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(44/27)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Sep 24 2018

%Y Cf. A009971 (denominators)

%K sign,frac

%O 0,2

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