A159494 Numerator of Hermite(n, 3/13).

1, 6, -302, -5868, 271020, 9559656, -400665864, -21790977552, 817229568912, 63826180714080, -2103055264345824, -228350822399665344, 6449054538439781568, 964885262883681324672, -22547834064602312261760, -4701124068353193901918464, 86110774297414559755612416

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..422

Crossrefs

Cf. A159280, A159488.

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(6/13)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 12 2018

Mathematica

Numerator[Table[HermiteH[n,3/13],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 14 2011 *)

PARI

a(n)=numerator(polhermite(n,3/13)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 12 2018: (Start)

a(n) = 13^n * Hermite(n,3/13).

E.g.f.: exp(6*x-169*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(6/13)^(n-2*k)/(k!*(n-2*k)!)). (End)