A159655 Numerator of Hermite(n, 17/19).

1, 34, 434, -34340, -2107604, 27515384, 8543973496, 171298455376, -37357094566000, -2259561093495776, 165921323311011616, 21955356087613897664, -571265042757181733696, -209644216596830988306560, -1766009672973345849952384, 2059039412479673870904327424

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Examples

			Numerator of 1, 34/19, 434/361, -34340/6859, -2107604/130321, 27515384/2476099,..
		

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)*(34/19)^(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

A159655 := proc(n)
        orthopoly[H](n,17/19) ;
        numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014

Mathematica

Numerator[Table[HermiteH[n, 17/19], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 16 2011 *)
Table[19^n*HermiteH[n, 17/19], {n,0,50}] (* G. C. Greubel, Jul 11 2018 *)

PARI

a(n)=numerator(polhermite(n,17/19)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

D-finite with recurrence a(n) -34*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, 17/19).

E.g.f.: exp(34*x - 361*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(34/19)^(n-2*k)/(k!*(n-2*k)!)). (End)