A158811 Numerator of Hermite(n, 1/3).

1, 2, -14, -100, 556, 8312, -33416, -964528, 2281360, 143454752, -82670816, -25987196992, -35605572416, 5542023405440, 19415750756224, -1357758396658432, -7957769497497344, 375118879242633728, 3185315224719454720, -115167886425174418432, -1319713579704402351104

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Examples

			Numerator of 1, 2/3, -14/9, -100/27, 556/81, 8312/243, -33416/729, -964528/2187, 2281360/6561, 143454752/19683, -82670816/59049,...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• DLMF Digital library of mathematical functions, Table 18.9.1 for H_n(x)

Crossrefs

Cf. A000244 (denominators).

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(2/3)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 09 2018

Maple

A158811 := proc(n)
        orthopoly[H](n,1/3) ;
        numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014

Mathematica

Numerator[Table[HermiteH[n,1/3],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Mar 23 2011 *)

PARI

a(n)=numerator(polhermite(n,1/3)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

D-finite with recurrence a(n) -2*a(n-1) +18*(n-1)*a(n-2)=0. [DLMF] - R. J. Mathar, Feb 16 2014

From G. C. Greubel, Jun 09 2018: (Start)

a(n) = 3^n * Hermite(n,1/3).

E.g.f.: exp(2*x-9*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(2/3)^(n-2*k)/(k!*(n-2*k)!)). (End)