A159524 - OEIS

%I #20 Sep 08 2022 08:45:43

%S 1,7,-79,-2345,13921,1298087,177169,-995690633,-7128577855,

%T 969687163207,14999931831409,-1136200046085097,-29073304341219551,

%U 1541690140398172135,59169809406576537809,-2348520065747488701257,-130045674520859373502079,3899449373004841245659783

%N Numerator of Hermite(n, 7/16).

%H Vincenzo Librandi, <a href="/A159524/b159524.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) -7*a(n-1) +128*(n-1)*a(n-2)=0. [DLMF] - _R. J. Mathar_, Feb 16 2014

%F From _G. C. Greubel_, Jun 09 2018: (Start)

%F a(n) = 16^n * Hermite(n,7/16).

%F E.g.f.: exp(14*x-252*x^2).

%F a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*(7/8)^(n-2k)/(k!*(n-2k)!). (End)

%e Numerator of 1, 7/8, -79/64, -2345/512, 13921/4096, 1298087/32768, 177169/262144,.

%p A159524 := proc(n)

%p         orthopoly[H](n,7/16) ;

%p         numer(%) ;

%p end proc: # _R. J. Mathar_, Feb 16 2014

%t Numerator[Table[HermiteH[n,7/16],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 29 2011 *)

%o (PARI) a(n)=numerator(polhermite(n,7/16)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(7/8)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jun 09 2018

%Y Cf. A001018 (denominators).

%K sign,frac

%O 0,2

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