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Numerator of Hermite(n, 4/29).
1

%I #15 Sep 08 2022 08:45:45

%S 1,8,-1618,-39856,7845580,330915808,-63334001336,-3846274345024,

%T 714924336969872,57474862282401920,-10362725714790706976,

%U -1049628989308325950208,183334119260591052868288,22652384474283979401944576,-3827564775957812126802428800

%N Numerator of Hermite(n, 4/29).

%H G. C. Greubel, <a href="/A160231/b160231.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, 4/29).

%F E.g.f.: exp(8*x - 841*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(8/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 8/29, -1618/841, -39856/24389, 7845580/707281.

%t Table[Numerator[HermiteH[n, 4/29]], {n, 0, 15}] (* _Wesley Ivan Hurt_, Jun 06 2014 *)

%t Table[29^n*HermiteH[n, 4/29], {n, 0, 30}] (* _G. C. Greubel_, Sep 26 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 4/29)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(8*x - 841*x^2))) \\ _G. C. Greubel_, Sep 26 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(8/29)^(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