A159280 Numerator of Hermite(n, 1/11).

1, 2, -238, -1444, 169900, 1737592, -202103816, -2927191216, 336509481872, 6340061157920, -720237529201376, -16783423060569152, 1883705456612924608, 52506471481118666624, -5821124423542023483520, -189534174225114089489152, 20751613309007317066199296

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Links

• T. D. Noe, Table of n, a(n) for n = 0..100

Crossrefs

The denominators are A001020.

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(2/22)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 08 2018

Mathematica

Numerator[Table[HermiteH[n,1/11],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 12 2011 *)

PARI

a(n)=polhermite(n,1/11)*11^n \\ Charles R Greathouse IV, Jun 20 2012

PARI

a(n)=numerator(polhermite(n,1/11)) \\ G. C. Greubel, Jun 08 2018

Python

from sympy import hermite
def a(n): return hermite(n, 1/11)*11**n # Indranil Ghosh, May 26 2017

Formula

From G. C. Greubel, Jun 08 2018: (Start)

a(n) = 11^n * Hermite(n,1/11).

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

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