A160139 - OEIS

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

%S 1,22,-974,-85580,2377516,551407912,-5201117576,-4938141000848,

%T -55556496038000,56376233721055072,1969289482873847584,

%U -778641119029758302912,-48713569344985450216256,12551406492954971362990720,1199447936209863593384712064

%N Numerator of Hermite(n, 11/27).

%H G. C. Greubel, <a href="/A160139/b160139.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, 11/27).

%F E.g.f.: exp(22*x - 729*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(22/27)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 22/27, -974/729, -85580/19683, 2377516/531441, ...

%t Numerator[HermiteH[Range[0,20],11/27]] (* _Harvey P. Dale_, Mar 06 2014 *)

%t Table[27^n*HermiteH[n, 11/27], {n, 0, 30}] (* _G. C. Greubel_, Sep 24 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 11/27)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(22*x - 729*x^2))) \\ _G. C. Greubel_, Sep 24 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(22/27)^(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