A159494 - OEIS

%I #12 Sep 08 2022 08:45:43

%S 1,6,-302,-5868,271020,9559656,-400665864,-21790977552,817229568912,

%T 63826180714080,-2103055264345824,-228350822399665344,

%U 6449054538439781568,964885262883681324672,-22547834064602312261760,-4701124068353193901918464,86110774297414559755612416

%N Numerator of Hermite(n, 3/13).

%H G. C. Greubel, <a href="/A159494/b159494.txt">Table of n, a(n) for n = 0..422</a>

%F From _G. C. Greubel_, Jun 12 2018: (Start)

%F a(n) = 13^n * Hermite(n,3/13).

%F E.g.f.: exp(6*x-169*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(6/13)^(n-2*k)/(k!*(n-2*k)!)). (End)

%t Numerator[Table[HermiteH[n,3/13],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 14 2011 *)

%o (PARI) a(n)=numerator(polhermite(n,3/13)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(6/13)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jun 12 2018

%Y Cf. A159280, A159488.

%K sign,frac

%O 0,2

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