A160284 - OEIS

%I #17 Sep 08 2022 08:45:45

%S 1,44,254,-136840,-7302644,599343184,87786336136,-2185972622944,

%T -1129779117074800,-20295833536956736,16209579598652226016,

%U 1054597422432310244224,-253507355147241835002176,-32440318000852390709512960,4115817835612084772939010176

%N Numerator of Hermite(n, 22/29).

%H G. C. Greubel, <a href="/A160284/b160284.txt">Table of n, a(n) for n = 0..371</a>

%F From _G. C. Greubel_, Oct 03 2018: (Start)

%F a(n) = 29^n * Hermite(n, 22/29).

%F E.g.f.: exp(44*x - 841*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(44/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 44/29, 254/841, -136840/24389, -7302644/707281, ...

%t Table[Numerator[HermiteH[n, 22/29]], {n, 0, 15}] (* _Wesley Ivan Hurt_, May 24 2014 *)

%t Table[29^n*HermiteH[n, 22/29], {n, 0, 30}] (* _G. C. Greubel_, Oct 03 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 22/29)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(44*x - 841*x^2))) \\ _G. C. Greubel_, Oct 03 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(44/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Oct 03 2018

%Y Cf. A009973 (denominators).

%K sign,frac

%O 0,2

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