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%I #13 Sep 08 2022 08:45:44
%S 1,13,-223,-13091,92065,21723533,101958529,-49768288739,-926761957183,
%T 144025448042125,5141947009489249,-497734445201769763,
%U -28642623292540648607,1968988727426096533261,171559661755326400233665,-8575534533295174571498723,-1120252760054156502803433599
%N Numerator of Hermite(n, 13/28).
%H G. C. Greubel, <a href="/A160196/b160196.txt">Table of n, a(n) for n = 0..417</a>
%F From _G. C. Greubel_, Sep 25 2018: (Start)
%F a(n) = 14^n * Hermite(n, 13/28).
%F E.g.f.: exp(13*x - 196*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(13/14)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerators of 1, 13/14, -223/196, -13091/2744, 92065/38416, ...
%t Table[14^n*HermiteH[n, 13/28], {n, 0, 30}] (* _G. C. Greubel_, Sep 25 2018 *)
%o (PARI) a(n)=numerator(polhermite(n, 13/28)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(13*x - 196*x^2))) \\ _G. C. Greubel_, Sep 25 2018
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(13/14)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Sep 25 2018
%Y Cf. A001023 (denominators).
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009
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