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%I #11 Sep 08 2022 08:45:45
%S 1,20,-1282,-92920,4610572,717377200,-24427366520,-7728318032800,
%T 133041452750480,106653076504366400,119080018350561760,
%U -1791523146436431612800,-38033681428250725939520,35399429559107921153964800,1539633069292288796472840320
%N Numerator of Hermite(n, 10/29).
%H G. C. Greubel, <a href="/A160253/b160253.txt">Table of n, a(n) for n = 0..371</a>
%F From _G. C. Greubel_, Sep 26 2018: (Start)
%F a(n) = 29^n * Hermite(n, 10/29).
%F E.g.f.: exp(20*x - 841*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(20/29)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerators of 1, 20/29, -1282/841, -92920/24389, 4610572/707281,...
%t Table[29^n*HermiteH[n, 10/29], {n, 0, 30}] (* _G. C. Greubel_, Sep 26 2018 *)
%o (PARI) a(n)=numerator(polhermite(n, 10/29)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(20*x - 841*x^2))) \\ _G. C. Greubel_, Sep 26 2018
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(20/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Sep 26 2018
%Y Cf. A009973 (denominators).
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009