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%I #13 Sep 08 2022 08:45:44
%S 1,5,-313,-4945,292657,8148925,-453845705,-18795248425,979822695905,
%T 55721465220725,-2702013314839385,-201848619020247425,
%U 9036842409471596305,863882210793481537325,-35388474493250786477545,-4264832993941008567009625,158095400711076444606105025
%N Numerator of Hermite(n, 5/26).
%H G. C. Greubel, <a href="/A160071/b160071.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, 5/26).
%F E.g.f.: exp(5*x - 169*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(5/13)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerators of 1, 5/13, -313/169, -4945/2197, 292657/28561, ...
%t Table[13^n*HermiteH[n, 5/26], {n, 0, 30}] (* _G. C. Greubel_, Sep 23 2018 *)
%o (PARI) a(n)=numerator(polhermite(n, 5/26)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(5*x - 169*x^2))) \\ _G. C. Greubel_, Sep 23 2018
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(5/13)^(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
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