A158960 Numerator of Hermite(n, 1/5).

1, 2, -46, -292, 6316, 71032, -1436936, -24183472, 454560656, 10582510112, -183387274976, -5658029605952, 89546942024896, 3573911647620992, -51057689020940416, -2603853531376575232, 33085559702952161536, 2149253944507164508672

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Comments

The denominators are 5^n = A000351(n) (conjectured). - M. F. Hasler, Feb 16 2014

Examples

			Numerators of 1, 2/5, -46/25, -292/125, 6316/625, 71032/3125, -1436936/15625,..
		

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)

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(2/5)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 02 2018

Maple

A158960 := proc(n)
    orthopoly[H](n,1/5) ;
    numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014

Mathematica

Numerator[Table[HermiteH[n,1/5],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Mar 23 2011*)

PARI

A158960 = n->numerator(polhermite(n,1/5)) \\ M. F. Hasler, Feb 16 2014

Formula

D-finite with recurrence a(n) -2*a(n-1) +50*(n-1)*a(n-2)=0. [DLMF] - R. J. Mathar, Feb 16 2014

a(n) = (-1)^floor(n/2)*2^ceiling(n/2)*A237987(n). - M. F. Hasler, Feb 16 2014

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

a(n) = 5^n * Hermite(n,1/5).

E.g.f.: exp(2*x-25*x^2).

a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*(2/5)^(n-2k)/(k!*(n-2k)!). (End)