A159654 Numerator of Hermite(n, 16/19).

1, 32, 302, -36544, -1823540, 47185792, 8092924744, 54564740864, -39155569948528, -1568144181583360, 204252279714867424, 17858073941907616768, -1050713239354433344832, -188345176292029458712576, 3834948823235768695790720, 2026511404303378366932021248

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Examples

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

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)*(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

Maple

A159654 := proc(n)
        orthopoly[H](n,16/19) ;
        numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014

Mathematica

Numerator[Table[HermiteH[n, 16/19], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 16 2011 *)
Table[19^n*HermiteH[n, 16/19], {n, 0, 50}] (* G. C. Greubel, Jul 11 2018 *)

PARI

a(n)=numerator(polhermite(n,16/19)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

D-finite with recurrence a(n) - 32*a(n-1) + 722*(n-1)*a(n-2) = 0. [DLMF] - R. J. Mathar, Feb 16 2014

From G. C. Greubel, Jul 11 2018: (Start)

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

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

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