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Numerator of Hermite(n, 3/5).
1

%I #14 Sep 08 2022 08:45:43

%S 1,6,-14,-684,-2004,124776,1249656,-29934864,-616988784,8272012896,

%T 327277030176,-2172344266944,-193036432198464,145187966975616,

%U 126344808730855296,656437275502200576,-90819982895128268544,-1070069717772530072064,70776567154223847830016

%N Numerator of Hermite(n, 3/5).

%H G. C. Greubel, <a href="/A158965/b158965.txt">Table of n, a(n) for n = 0..450</a>

%F From _G. C. Greubel_, Jun 02 2018: (Start)

%F a(n) = 5^n * Hermite(n, 3/5).

%F E.g.f.: exp(6*x - 25*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(6/5)^(n-2*k)/(k!*(n-2*k)!)). (End)

%t Numerator[Table[HermiteH[n,3/5],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 01 2011*)

%t Table[5^n*HermiteH[n, 3/5], {n,0,30}] (* _G. C. Greubel_, Jul 13 2018 *)

%o (PARI) a(n)=numerator(polhermite(n,3/5)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(6*x - 25*x^2))) \\ _G. C. Greubel_, Jul 13 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(6/5)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 13 2018

%Y Cf. A158960, A158961.

%K sign,frac

%O 0,2

%A _N. J. A. Sloane_, Nov 12 2009