A158987 Numerator of Hermite(n, 3/7).

1, 6, -62, -1548, 8940, 660456, -417864, -390855312, -2058477168, 294079701600, 3580055071776, -266717777137344, -5459606030198592, 280902469732324992, 8640952900866956160, -333552471067548152064, -14703515590679714467584, 434789181089837215630848

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Examples

			Numerator of 1, 6/7, -62/49, -1548/343, 8940/2401, 660456/16807, -417864/117649, ...
		

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. A000420 (denominators).

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(6/7)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 09 2018

Maple

A158987 := proc(n)
        orthopoly[H](n,3/7) ;
        numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014

Mathematica

Numerator[Table[HermiteH[n,3/7],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Mar 23 2011 *)
Table[7^n*HermiteH[n, 3/7], {n,0,30}] (* G. C. Greubel, Jul 09 2018 *)

PARI

a(n)=numerator(polhermite(n,3/7)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

D-finite with recurrence a(n) - 6*a(n-1) + 98*(n-1)*a(n-2) = 0. [DLMF] - R. J. Mathar, Feb 16 2014

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

a(n) = 7^n * Hermite(n, 3/7).

E.g.f.: exp(6*x-49*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(6/7)^(n-2*k)/(k!*(n-2*k)!)). (End)