%I #11 Sep 08 2022 08:45:44
%S 1,7,-289,-6755,245761,10853087,-339364481,-24385611803,632237079425,
%T 70364353871287,-1430714718511841,-247846519114532947,
%U 3584471689625294209,1030356783355922692495,-8537671120722083906881,-4935411996685280768234507,8738108605264000030245121
%N Numerator of Hermite(n, 7/26).
%H G. C. Greubel, <a href="/A160072/b160072.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, 7/26).
%F E.g.f.: exp(7*x - 169*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(7/13)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerators of 1, 7/13, -289/169, -6755/2197, 245761/28561
%t Table[13^n*HermiteH[n, 7/26], {n, 0, 30}] (* _G. C. Greubel_, Sep 23 2018 *)
%o (PARI) a(n)=numerator(polhermite(n, 7/26)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(7*x - 169*x^2))) \\ _G. C. Greubel_, Sep 23 2018
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(7/13)^(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