A159450 - OEIS

%I #11 Sep 08 2022 08:45:43

%S 1,14,-46,-7420,-70484,6195784,172026616,-6587905744,-383643767920,

%T 7383172769504,938940545302816,-4722110467960256,-2565569278147539776,

%U -22204961095108973440,7760411493720634507136,183876169102318085114624,-25596027354773450069298944

%N Numerator of Hermite(n, 7/11).

%H G. C. Greubel, <a href="/A159450/b159450.txt">Table of n, a(n) for n = 0..435</a>

%F From _G. C. Greubel_, Jun 15 2018: (Start)

%F a(n) = 11^n * Hermite(n,7/11).

%F E.g.f.: exp(14*x-121*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(14/11)^(n-2*k)/(k!*(n-2*k)!)). (End)

%t Numerator[Table[HermiteH[n,7/11],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 12 2011 *)

%o (PARI) a(n)=numerator(polhermite(n,7/11)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(14/11)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jun 15 2018

%Y Cf. A159280.

%K sign,frac

%O 0,2

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