|
%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
|
