A159520 - OEIS

%I #21 Sep 08 2022 08:45:43

%S 1,28,334,-15848,-894644,3476368,2110287304,49701850912,

%T -5255753182064,-326087752380992,12155343320691424,

%U 1807744498693823872,-9552103473995480384,-10029279190218522359552,-224940012003245065821056,56886138562285829022188032

%N Numerator of Hermite(n, 14/15).

%H Vincenzo Librandi, <a href="/A159520/b159520.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) -28*a(n-1) +450*(n-1)*a(n-2)=0. [DLMF] - _R. J. Mathar_, Feb 16 2014

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

%F a(n) = 15^n * Hermite(n,14/15).

%F E.g.f.: exp(28*x-225*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(28/15)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 28/15, 334/225, -15848/3375, -894644/50625, 3476368/759375

%p A159520 := proc(n)

%p         orthopoly[H](n,14/15) ;

%p         numer(%) ;

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

%t Numerator[Table[HermiteH[n,14/15],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 28 2011 *)

%o (PARI) a(n)=numerator(polhermite(n,14/15)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(28/15)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jun 11 2018

%Y Cf. A001024 (denominators).

%K sign,frac

%O 0,2

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