A159326 Numerator of Hermite(n, 4/11).

1, 8, -178, -5296, 86860, 5821408, -58529336, -8920919104, 27781342352, 17493150124160, 79437437350624, -41697923801662208, -545045848640658752, 116730403930901782016, 2648557471270726689920, -374294148747729423950848, -12608616810694573276016384

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..434

Crossrefs

Cf. A159280.

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(8/11)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 26 2018

Magma

I:=[1, 8]; [n le 2 select I[n] else 8*Self(n-1)-242*(n-2)*Self(n-2): n in [1..25]]; // Vincenzo Librandi, Jun 27 2018

Mathematica

Numerator[Table[HermiteH[n,4/11],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 12 2011 *)

PARI

a(n)=numerator(polhermite(n,4/11)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 26 2018: (Start)

a(n) = 11^n * Hermite(n, 8/11).

E.g.f.: exp(8*x - 121*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(8/11)^(n-2*k)/(k!*(n-2*k)!)). (End)

a(n) = 8*a(n-1) - 242*(n-1)*a(n-2) for n>1. - Vincenzo Librandi, Jun 27 2018 [corrected by Georg Fischer, Dec 23 2019]