A159281 Numerator of Hermite(n, 2/11).

1, 4, -226, -2840, 152716, 3359984, -171346424, -5564082464, 268004512400, 11844081699904, -536337501207584, -30808027718598016, 1304498317340196544, 94684505764169424640, -3725213683295580628864, -335691960262188333195776, 12179757829314204349993216

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Comments

Denominator is 11^n. - Robert Israel, May 21 2014

Links

• G. C. Greubel, Table of n, a(n) for n = 0..434 (terms 0..82 from Robert Israel)

Crossrefs

Cf. A159280.

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(4/11)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 27 2018

Maple

N:= 30; # to get a(n) for n <= N
A159281[0]:= 1:
A159281[1]:= 4:
for n from 2 to N do
  A159281[n]:= 4*A159281[n-1] - 242*(n-1)*A159281[n-2]
od:
seq(A159281[n],n=0..N); # Robert Israel, May 21 2014

Mathematica

Numerator[Table[HermiteH[n,2/11],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 12 2011 *)

PARI

a(n)=numerator(polhermite(n,2/11)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

a(n) = 4*a(n-1) - 242*(n-1)*a(n-2) for n >= 2.

E.g.f.: exp(-11*x^2 + 4*x). - Robert Israel, May 21 2014

From G. C. Greubel, Jun 27 2018: (Start)

a(n) = 11^n * Hermite(n, 2/11).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(4/11)^(n-2*k)/(k!*(n-2*k)!)). (End)