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Numerator of Hermite(n, 1/15).
6

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

%S 1,2,-446,-2692,596716,6039032,-1330532936,-18966452272,4153245843856,

%T 76585719866912,-16667474227882976,-377970687856869952,

%U 81748056052306991296,2204537826531711723392,-473817052252932475634816,-14836222411655648808639232,3168592657883982912917729536

%N Numerator of Hermite(n, 1/15).

%H G. C. Greubel, <a href="/A159513/b159513.txt">Table of n, a(n) for n = 0..412</a>

%F From _G. C. Greubel_, Jun 09 2018: (Start)

%F a(n) = 15^n * Hermite(n,1/15).

%F E.g.f.: exp(2*x-225*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(2/15)^(n-2k)/(k!*(n-2k)!)). (End)

%t Numerator[Table[HermiteH[n,1/15],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 28 2011 *)

%o (PARI) a(n)=numerator(polhermite(n,1/15)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(2/15)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jun 09 2018

%Y Cf. A159512.

%K sign,frac

%O 0,2

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