A160087 - OEIS

%I #11 Sep 08 2022 08:45:44

%S 1,2,-1454,-8740,6342316,63656312,-46108171016,-649081759408,

%T 469281829870480,8509453301475872,-6140897264957486816,

%U -136349623665433187392,98215011088057307180224,2582003037826533660970880,-1856403314087385132972023936

%N Numerator of Hermite(n, 1/27).

%H G. C. Greubel, <a href="/A160087/b160087.txt">Table of n, a(n) for n = 0..376</a>

%F From _G. C. Greubel_, Sep 23 2018: (Start)

%F a(n) = 27^n * Hermite(n, 1/27).

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

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

%e Numerators of 1, 2/27, -1454/729, -8740/19683, 6342316/531441..

%t Table[27^n*HermiteH[n, 1/27], {n, 0, 30}] (* _G. C. Greubel_, Sep 23 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 1/27)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(2*x - 729*x^2))) \\ _G. C. Greubel_, Sep 23 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(2/27)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Sep 23 2018

%Y Cf. A009971 (denominators).

%K sign,frac

%O 0,2

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