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

%S 1,26,-782,-96148,920620,584671256,8490132856,-4893960693232,

%T -213893273952368,51521932403096480,4146277783283481376,

%U -643386552071776162624,-83226053442166654536512,9092813725551462723320192,1813879773807164800891373440

%N Numerator of Hermite(n, 13/27).

%H G. C. Greubel, <a href="/A160140/b160140.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, 13/27).

%F E.g.f.: exp(26*x - 729*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(26/27)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 26/27, -782/729, -96148/19683, 920620/531441

%t Table[27^n*HermiteH[n, 13/27], {n, 0, 30}] (* _G. C. Greubel_, Sep 24 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 13/27)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(26*x - 729*x^2))) \\ _G. C. Greubel_, Sep 24 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(26/27)^(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