A160287 - OEIS

%I #15 Sep 08 2022 08:45:45

%S 1,50,818,-127300,-10492628,331843000,104835151480,1892798018000,

%T -1139689172625520,-82453948761484000,13129917257130921760,

%U 2043371281024706968000,-140761165040200966003520,-48281464188212733742288000,663810425358397635518568320

%N Numerator of Hermite(n, 25/29).

%H G. C. Greubel, <a href="/A160287/b160287.txt">Table of n, a(n) for n = 0..372</a>

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

%F a(n) = 29^n * Hermite(n, 25/29).

%F E.g.f.: exp(50*x - 841*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(50/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 50/29, 818/841, -127300/24389, -10492628/707281, ...

%t Numerator[HermiteH[Range[0,20],25/29]] (* _Harvey P. Dale_, Dec 05 2012 *)

%t Table[29^n*HermiteH[n, 25/29], {n, 0, 30}] (* _G. C. Greubel_, Oct 03 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 25/29)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(50*x - 841*x^2))) \\ _G. C. Greubel_, Oct 03 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(50/29)^(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