%I #15 Sep 08 2022 08:45:44
%S 1,3,-329,-3015,324561,5049963,-533358201,-11841399567,1226401304865,
%T 35698348343763,-3623617724368041,-131531270575023063,
%U 13078016887475307249,572724884114719465275,-55746631551222341656281,-2877374046284519534650143,274003299825843713593394241
%N Numerator of Hermite(n, 3/26).
%H G. C. Greubel, <a href="/A160070/b160070.txt">Table of n, a(n) for n = 0..423</a>
%F From _G. C. Greubel_, Sep 23 2018: (Start)
%F a(n) = 13^n * Hermite(n, 3/26).
%F E.g.f.: exp(3*x - 169*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(3/13)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerators of 1, 3/13, -329/169, -3015/2197, 324561/28561, ...
%t Numerator[HermiteH[Range[0,20],3/26]] (* _Harvey P. Dale_, Jun 11 2018 *)
%t Table[13^n*HermiteH[n, 3/26], {n, 0, 30}] (* _G. C. Greubel_, Sep 23 2018 *)
%o (PARI) a(n)=numerator(polhermite(n, 3/26)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(3*x - 169*x^2))) \\ _G. C. Greubel_, Sep 23 2018
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(3/13)^(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. A001022 (denominators).
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009