A159502 Numerator of Hermite(n, 9/13).

1, 18, -14, -12420, -209364, 13023288, 588244344, -15822829872, -1676597055600, 12606184973088, 5327119572650784, 53279247098676672, -18847204123339434816, -555350300452342408320, 72818309509811313231744, 3938647192917087914341632, -298293179742235775626792704

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)*(18/13)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 11 2018

Mathematica

Numerator[Table[HermiteH[n,9/13],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 14 2011 *)

PARI

a(n)=numerator(polhermite(n,9/13)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

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

a(n) = 13^n * Hermite(n,9/13).

E.g.f.: exp(18*x-169*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(18/13)^(n-2*k)/(k!*(n-2*k)!)). (End)