A159648 Numerator of Hermite(n, 10/19).

1, 20, -322, -35320, -8948, 101825200, 2068806280, -399730640800, -18450359755120, 1939836986158400, 158687177411937760, -10831879491824892800, -1476931152842107545920, 64308780860328720300800, 15148651417782595832021120, -347060128580550788160064000

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Examples

			Numerator of 1, 20/19, -322/361, -35320/6859, -8948/130321, 101825200/2476099, ...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• DLMF Digital library of mathematical functions, Table 18.9.1 for H_n(x)

Crossrefs

Cf. A001029 (denominators).

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(20/19)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 10 2018

Maple

A159648 := proc(n)
        orthopoly[H](n,10/19) ;
        numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014

Mathematica

Numerator[Table[HermiteH[n,10/19],{n,0,30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 16 2011 *)
Table[19^n*HermiteH[n, 10/19], {n,0,50}] (* G. C. Greubel, Jul 10 2018 *)

PARI

a(n)=numerator(polhermite(n,10/19)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

D-finite with recurrence a(n) - 20*a(n-1) + 722*(n-1)*a(n-2) = 0. [DLMF] - R. J. Mathar, Feb 16 2014

From G. C. Greubel, Jul 10 2018: (Start)

a(n) = 19^n * Hermite(n, 10/19).

E.g.f.: exp(20*x - 361*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(20/19)^(n-2*k)/(k!*(n-2*k)!)). (End)