A159676 - OEIS

%I #19 Sep 08 2022 08:45:44

%S 1,17,89,-5287,-143279,1793857,173774569,801539273,-229658228959,

%T -5186652729103,325211715731449,15901904625640633,-445133395973297039,

%U -45731838833083568863,379905569368151630729,134507543411892570538793,1146911529897718806972481

%N Numerator of Hermite(n, 17/20).

%H Vincenzo Librandi, <a href="/A159676/b159676.txt">Table of n, a(n) for n = 0..200</a>

%H DLMF <a href="https://dlmf.nist.gov/18.9">Digital library of mathematical functions</a>, Table 18.9.1 for H_n(x)

%F D-finite with recurrence a(n) -17*a(n-1) +200*(n-1)*a(n-2)=0. [DLMF] - _R. J. Mathar_, Feb 17 2014

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

%F a(n) = 10^n * Hermite(n, 17/20).

%F E.g.f.: exp(17*x - 100*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(17/10)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerator of 1, 17/10, 89/100, -5287/1000, -143279/10000, 1793857/100000,...

%p A159676 := proc(n)

%p         orthopoly[H](n,17/20) ;

%p         numer(%) ;

%p end proc: # _R. J. Mathar_, Feb 17 2014

%t Numerator/@Table[HermiteH[n,17/20],{n,0,35}]  (* _Harvey P. Dale_, Mar 13 2011 *)

%t Table[10^n*HermiteH[n, 17/20], {n,0,50}] (* _G. C. Greubel_, Jul 11 2018 *)

%o (PARI) a(n)=numerator(polhermite(n,17/20)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(17/10)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 11 2018

%Y Cf. A011557 (denominators).

%K sign,frac

%O 0,2

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