A159531 Numerator of Hermite(n, 3/17).

1, 6, -542, -10188, 878700, 28826856, -2366481864, -114170427792, 8889763054992, 581262636440160, -42756971593427424, -3616239868184689344, 250151386181903425728, 26583148042820425844352, -1720138627513899785854080, -225431665727586284647620864

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Links

• G. C. Greubel, Table of n, a(n) for n = 0..404

Crossrefs

Cf. A159521, A159529, A159530.

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(6/17)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 09 2018

Mathematica

Numerator[Table[HermiteH[n,3/17],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 29 2011 *)
Table[17^n*HermiteH[n, 3/17], {n,0,30}] (* G. C. Greubel, Jul 09 2018 *)

PARI

a(n)=numerator(polhermite(n,3/17)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jul 09 2018: (Start)

a(n) = 17^n * Hermite(n, 3/17).

E.g.f.: exp(6*x-289*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(6/17)^(n-2*k)/(k!*(n-2*k)!)). (End)