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%I #11 Sep 08 2022 08:45:45
%S 1,2,-1678,-10084,8447020,84739192,-70869959816,-996927845296,
%T 832429051182992,15079519188668960,-12571151938430794976,
%U -278779816630273497152,232033893531586021651648,6090959605928612309819264,-5061471196749802724815296640
%N Numerator of Hermite(n, 1/29).
%H G. C. Greubel, <a href="/A160224/b160224.txt">Table of n, a(n) for n = 0..372</a>
%F From _G. C. Greubel_, Sep 26 2018: (Start)
%F a(n) = 29^n * Hermite(n, 1/29).
%F E.g.f.: exp(2*x - 841*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(2/29)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerators of 1, 2/29, -1678/841, -10084/24389, 8447020/707281..
%t Table[29^n*HermiteH[n, 2/29], {n, 0, 30}] (* _G. C. Greubel_, Sep 26 2018 *)
%o (PARI) a(n)=numerator(polhermite(n, 1/29)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(2*x - 841*x^2))) \\ _G. C. Greubel_, Sep 26 2018
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(2/29)^(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
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