A159492 - OEIS

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

%S 1,4,-322,-3992,310540,6639344,-498255224,-15457610528,1117041417872,

%T 46265544539200,-3212977815009824,-169229451802535296,

%U 11268933708996384448,731470391347068698368,-46589813151941838471040,-3647677144462096434561536,221619644102496735309926656

%N Numerator of Hermite(n, 2/13).

%H G. C. Greubel, <a href="/A159492/b159492.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, 2/13).

%F E.g.f.: exp(4*x-169*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(4/13)^(n-2*k)/(k!*(n-2*k)!)). (End)

%t Numerator[Table[HermiteH[n,2/13],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 13 2011 *)

%o (PARI) a(n)=numerator(polhermite(n,2/13)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(4/13)^(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