The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A159019 Numerator of Hermite(n, 5/8). 1

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

%S 1,5,-7,-355,-1103,39925,376105,-5785075,-113172895,915114725,

%T 37169367385,-106989875075,-13618566694895,-27008721445675,

%U 5530280137847945,39751307896902125,-2455777926682502975,-32631559276626402875,1172785395732149604025

%N Numerator of Hermite(n, 5/8).

%H G. C. Greubel, <a href="/A159019/b159019.txt">Table of n, a(n) for n = 0..450</a>

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

%F a(n) = 4^n * Hermite(n, 5/8).

%F E.g.f.: exp(5*x - 16*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(5/4)^(n-2*k)/(k!*(n-2*k)!)). (End)

%t Numerator[Table[HermiteH[n,5/8],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 01 2011 *)

%t Table[4^n*HermiteH[n, 5/8], {n,0,30}] (* _G. C. Greubel_, Jul 14 2018 *)

%o (PARI) a(n)=numerator(polhermite(n,5/8)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(5*x - 16*x^2))) \\ _G. C. Greubel_, Jul 14 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(5/4)^(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. A159014, A159017.

%K sign,frac

%O 0,2

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 13 10:14 EDT 2024. Contains 375904 sequences. (Running on oeis4.)