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%I #13 Sep 08 2022 08:45:45
%S 1,7,-401,-9107,477601,19735807,-936451601,-59841840107,2530929662401,
%T 233147132022007,-8618235208570001,-1109489740559021507,
%U 34893836098508354401,6235501451708274618607,-160480431014315950915601,-40407022162862341753633307,800393754206596276404873601
%N Numerator of Hermite(n, 7/30).
%H G. C. Greubel, <a href="/A160292/b160292.txt">Table of n, a(n) for n = 0..412</a>
%F From _G. C. Greubel_, Oct 03 2018: (Start)
%F a(n) = 15^n * Hermite(n, 7/30).
%F E.g.f.: exp(7*x - 225*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(7/15)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerators of 1, 7/15, -401/225, -9107/3375, 477601/50625, ...
%t Table[15^n*HermiteH[n, 7/30], {n, 0, 30}] (* _G. C. Greubel_, Oct 03 2018 *)
%o (PARI) a(n)=numerator(polhermite(n, 7/30)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(7*x - 225*x^2))) \\ _G. C. Greubel_, Oct 03 2018
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(7/15)^(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. A001024 (denominators).
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009
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