A159654 - OEIS

%I #22 Sep 08 2022 08:45:44

%S 1,32,302,-36544,-1823540,47185792,8092924744,54564740864,

%T -39155569948528,-1568144181583360,204252279714867424,

%U 17858073941907616768,-1050713239354433344832,-188345176292029458712576,3834948823235768695790720,2026511404303378366932021248

%N Numerator of Hermite(n, 16/19).

%H Vincenzo Librandi, <a href="/A159654/b159654.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) - 32*a(n-1) + 722*(n-1)*a(n-2) = 0. [DLMF] - _R. J. Mathar_, Feb 16 2014

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

%F a(n) = 19^n * Hermite(n, 16/19).

%F E.g.f.: exp(32*x - 361*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(32/19)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerator of 1, 32/19, 302/361, -36544/6859, -1823540/130321, 47185792/2476099, ...

%p A159654 := proc(n)

%p         orthopoly[H](n,16/19) ;

%p         numer(%) ;

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

%t Numerator[Table[HermiteH[n, 16/19], {n, 0, 30}]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 16 2011 *)

%t Table[19^n*HermiteH[n, 16/19], {n, 0, 50}] (* _G. C. Greubel_, Jul 11 2018 *)

%o (PARI) a(n)=numerator(polhermite(n,16/19)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(32/19)^(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. A001029 (denominators).

%K sign,frac

%O 0,2

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