A159460 - OEIS

%I #22 Sep 08 2022 08:45:43

%S 1,18,82,-7236,-189780,3588408,294225144,85684176,-496875078768,

%T -9109635982560,918220473870624,38573287607466432,

%U -1749983724509205312,-143516534253248214144,2922151180747492056960,538832739303459806545152,-908419478651119648952064

%N Numerator of Hermite(n, 9/11).

%H Vincenzo Librandi, <a href="/A159460/b159460.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) - 18*a(n-1) + 242*(n-1)*a(n-2) = 0. [DLMF] - _R. J. Mathar_, Feb 16 2014

%F From _G. C. Greubel_, Jun 15 2018: (Start)

%F a(n) = 11^n * Hermite(n,9/11).

%F E.g.f.: exp(18*x-121*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(18/11)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerator of 1, 18/11, 82/121, -7236/1331, -189780/14641, 3588408/161051, ...

%p A159460 := proc(n)

%p         orthopoly[H](n,9/11) ;

%p         numer(%) ;

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

%t Numerator[Table[HermiteH[n,9/11],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 13 2011 *)

%o (PARI) a(n)=numerator(polhermite(n,9/11)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(18/11)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jun 15 2018

%Y Cf. A001020 (denominators).

%K sign,frac

%O 0,2

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