A159705 Numerator of Hermite(n, 1/21).

1, 2, -878, -5284, 2312620, 23267192, -10152119816, -143434219696, 62392319304592, 1136856492784160, -492996517654282976, -11013067301664857152, 4761026079678523718848, 126084356480177895534464, -54337756316633597169242240, -1665565146450503848398045952

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Examples

			Numerator of 1, 2/21, -878/441, -5284/9261, 2312620/194481, 23267192/4084101, ...
		

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. A009965 (denominators).

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(2/21)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, May 21 2018

Maple

A159705 := proc(n)
        orthopoly[H](n,1/21) ;
        numer(%) ;
end proc: # R. J. Mathar, Feb 17 2014

Mathematica

Numerator[Table[HermiteH[n, 1/21], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 17 2011 *)

PARI

a(n)=numerator(polhermite(n,1/21)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

D-finite with recurrence a(n) - 2*a(n-1) + 882*(n-1)*a(n-2) = 0. [DLMF] - R. J. Mathar, Feb 17 2014

From G. C. Greubel, May 22 2018: (Start)

a(n) = 21^n * Hermite(n,1/21).

E.g.f.: exp(2*x-441*x^2).

a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*(2/21)^(n-2k)/(k!*(n-2k)!). (End)