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%I #13 Sep 08 2022 08:45:44
%S 1,9,-257,-8397,185025,13017969,-195530529,-28160215893,209183288577,
%T 78027873371865,65915296495551,-263140974328443741,
%U -2613341841326452287,1043779715304229742913,20877041488526499035295,-4751272239422876652146661,-148608050501635239978265599
%N Numerator of Hermite(n, 9/26).
%H G. C. Greubel, <a href="/A160073/b160073.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, 9/26).
%F E.g.f.: exp(9*x - 169*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(9/13)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerators of 1, 9/13, -257/169, -8397/2197, 185025/28561
%t Numerator[HermiteH[Range[0,20],9/26]] (* _Harvey P. Dale_, Jul 18 2015 *)
%t Table[13^n*HermiteH[n, 9/26], {n, 0, 30}] (* _G. C. Greubel_, Sep 23 2018 *)
%o (PARI) a(n)=numerator(polhermite(n, 9/26)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(9*x - 169*x^2))) \\ _G. C. Greubel_, Sep 23 2018
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(9/13)^(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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