A159005 - OEIS

%I #13 Sep 08 2022 08:45:43

%S 1,10,2,-1940,-19988,560600,15400120,-175631600,-12320798320,

%T 14487191200,11011816030240,95920712926400,-10911530551334720,

%U -221918063914793600,11682109283252497280,421292676523621792000,-12959773881144953081600

%N Numerator of Hermite(n, 5/7).

%H G. C. Greubel, <a href="/A159005/b159005.txt">Table of n, a(n) for n = 0..450</a>

%F From _G. C. Greubel_, Jul 14 2018: (Start)

%F a(n) = 7^n * Hermite(n, 5/7).

%F E.g.f.: exp(10*x - 49*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(10/7)^(n-2*k)/(k!*(n-2*k)!)). (End)

%t Numerator[Table[HermiteH[n,5/7],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 01 2011*)

%t Table[7^n*HermiteH[n, 5/7], {n,0,30}] (* _G. C. Greubel_, Jul 14 2018 *)

%o (PARI) a(n)=numerator(polhermite(n,5/7)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(10*x - 49*x^2))) \\ _G. C. Greubel_, Jul 14 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(10/7)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 14 2018

%Y Cf. A158980.

%K sign,frac

%O 0,2

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