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%I #11 Sep 08 2022 08:45:44
%S 1,25,287,-9725,-534143,-205375,897567295,22855682875,-1552252148095,
%T -100608070196375,2206749279595615,395224009253637875,
%U 1675906409804450305,-1561130921287643963375,-46392205796871853724545,6227466374611334891576875,390895142755423670672865025
%N Numerator of Hermite(n, 25/26).
%H G. C. Greubel, <a href="/A160084/b160084.txt">Table of n, a(n) for n = 0..422</a>
%F From _G. C. Greubel_, Sep 23 2018: (Start)
%F a(n) = 13^n * Hermite(n, 25/26).
%F E.g.f.: exp(25*x - 169*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(25/13)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerators of 1, 25/13, 287/169, -9725/2197, -534143/28561..
%t Table[13^n*HermiteH[n, 25/26], {n, 0, 30}] (* _G. C. Greubel_, Sep 23 2018 *)
%o (PARI) a(n)=numerator(polhermite(n, 25/26)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(25*x - 169*x^2))) \\ _G. C. Greubel_, Sep 23 2018
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(25/13)^(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