A159652 - OEIS

%I #24 Sep 08 2022 08:45:44

%S 1,28,62,-38696,-1217780,77656208,6570559624,-152431023584,

%T -37475677000048,-168877363780160,238788382960467424,

%U 7905369289385843072,-1675106997369228675392,-115395115449577347286784,12491491044719414623199360,1516175576216471435824394752

%N Numerator of Hermite(n, 14/19).

%H Vincenzo Librandi, <a href="/A159652/b159652.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) +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, 14/19).

%F E.g.f.: exp(28*x - 361*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(28/19)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerator of 1, 28/19, 62/361, -38696/6859, -1217780/130321, 77656208/2476099, ...

%p A159652 := proc(n)

%p         orthopoly[H](n,14/19) ;

%p         numer(%) ;

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

%t Numerator[Table[HermiteH[n, 14/19], {n, 0, 30}]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 16 2011 *)

%t Table[19^n*HermiteH[n, 14/19], {n,0,50}] (* _G. C. Greubel_, Jul 11 2018 *)

%o (PARI) a(n)=numerator(polhermite(n,14/19)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(28/19)^(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