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%I #16 Sep 08 2022 08:45:45
%S 1,54,1234,-115020,-12437844,102210984,110121661176,4915056452976,
%T -1031159390225520,-121819606703423136,9031432087249072416,
%U 2536703117463027057984,-30117588135278876709696,-52827165482178797480672640,-2194115753871647145822109824
%N Numerator of Hermite(n, 27/29).
%H G. C. Greubel, <a href="/A160289/b160289.txt">Table of n, a(n) for n = 0..372</a>
%F From _G. C. Greubel_, Oct 03 2018: (Start)
%F a(n) = 29^n * Hermite(n, 27/29).
%F E.g.f.: exp(54*x - 841*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(54/29)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerators of 1, 54/29, 1234/841, -115020/24389, -12437844/707281, ...
%t Numerator[HermiteH[Range[0,20],27/29]] (* _Harvey P. Dale_, Sep 02 2011 *)
%t Table[29^n*HermiteH[n, 27/29], {n, 0, 30}] (* _G. C. Greubel_, Oct 03 2018 *)
%o (PARI) a(n)=numerator(polhermite(n, 27/29)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(54*x - 841*x^2))) \\ _G. C. Greubel_, Oct 03 2018
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(54/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Oct 03 2018
%Y Cf. A009973 (denominators).
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009
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