A159512 - OEIS

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

%S 1,13,71,-1625,-41999,91013,21762679,229399183,-11947008415,

%T -335160068867,6180180526759,408799214337527,-1347844821458351,

%U -498269858739890315,-4760353861080634921,621741645997081258207,15080361573750589690561

%N Numerator of Hermite(n, 13/14).

%H G. C. Greubel, <a href="/A159512/b159512.txt">Table of n, a(n) for n = 0..450</a>

%F From _G. C. Greubel_, Jun 11 2018: (Start)

%F a(n) = 7^n * Hermite(n,13/14).

%F E.g.f.: exp(13*x-49*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(13/7)^(n-2*k)/(k!*(n-2*k)!)). (End)

%t Numerator[Table[HermiteH[n,13/14],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 28 2011 *)

%o (PARI) a(n)=numerator(polhermite(n,13/14)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(13/7)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jun 11 2018

%Y Cf. A159507, A159508, A159509.

%K sign,frac

%O 0,2

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