A159663 - OEIS

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

%S 1,11,-79,-5269,-10559,4099051,55648561,-4306727029,-125281982719,

%T 5512661436491,286146844695601,-7877707581330389,-716177841724956479,

%U 11028541936218412331,1983376349783289381041,-9062777573795371335349,-6049819602661617227811839

%N Numerator of Hermite(n, 11/20).

%H Vincenzo Librandi, <a href="/A159663/b159663.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) -11*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, 11/20).

%F E.g.f.: exp(11*x - 100*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(11/10)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerator of 1, 11/10, -79/100, -5269/1000, -10559/10000, 4099051/100000,..

%p A159663 := proc(n)

%p         orthopoly[H](n,11/20) ;

%p         numer(%) ;

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

%t Numerator[Table[HermiteH[n, 11/20], {n, 0, 30}]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 16 2011 *)

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

%o (PARI) a(n)=numerator(polhermite(n,11/20)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(11/10)^(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