A160151 - OEIS

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

%S 1,46,658,-103868,-7656020,253581256,67477123576,885618857008,

%T -647933055794288,-40134778914678560,6655977728057433376,

%U 891340052066655340096,-65746928407518970839872,-18619244257704074488953728,389682045181727146807062400

%N Numerator of Hermite(n, 23/27).

%H G. C. Greubel, <a href="/A160151/b160151.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, 23/27).

%F E.g.f.: exp(46*x - 729*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(46/27)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 46/27, 658/729, -103868/19683, -7656020/531441, ...

%t Table[27^n*HermiteH[n, 23/27], {n, 0, 30}] (* _G. C. Greubel_, Sep 24 2018 *)

%t HermiteH[Range[0,20],23/27]//Numerator (* _Harvey P. Dale_, Jan 02 2019 *)

%o (PARI) a(n)=numerator(polhermite(n, 23/27)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(46*x - 729*x^2))) \\ _G. C. Greubel_, Sep 24 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(46/27)^(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