%I #14 Sep 08 2022 08:45:44

%S 1,52,1246,-86840,-9965684,-11764688,72038072584,3848897264992,

%T -535077911012720,-72717589071528128,3239977716589449184,

%U 1228701289925531463808,11929704457466050105024,-20877013136748863885323520,-1311720301397752435727447936

%N Numerator of Hermite(n, 26/27).

%H G. C. Greubel, <a href="/A160153/b160153.txt">Table of n, a(n) for n = 0..376</a>

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

%F a(n) = 27^n * Hermite(n, 26/27).

%F E.g.f.: exp(52*x - 729*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(52/27)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 52/27, 1246/729, -86840/19683, -9965684/531441, ...

%t Table[27^n*HermiteH[n, 26/27], {n, 0, 30}] (* _G. C. Greubel_, Sep 24 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 26/27)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(52*x - 729*x^2))) \\ _G. C. Greubel_, Sep 24 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(52/27)^(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