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%I #13 Sep 08 2022 08:45:45
%S 1,30,-782,-124380,214572,843265800,23493423480,-7805435749200,
%T -510774640529520,89706704225349600,10423307635096361760,
%U -1196167536017489419200,-228737063945077567859520,17281333628624679401347200,5520004649081806480856680320
%N Numerator of Hermite(n, 15/29).
%H G. C. Greubel, <a href="/A160269/b160269.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, 15/29).
%F E.g.f.: exp(30*x - 841*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(30/29)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerators of 1, 30/29, -782/841, -124380/24389, 214572/707281,...
%t Numerator[HermiteH[Range[0,20],15/29]] (* _Harvey P. Dale_, Dec 12 2012 *)
%t Table[29^n*HermiteH[n, 15/29], {n, 0, 30}] (* _G. C. Greubel_, Sep 26 2018 *)
%o (PARI) a(n)=numerator(polhermite(n, 15/29)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(30*x - 841*x^2))) \\ _G. C. Greubel_, Sep 26 2018
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(30/29)^(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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