A158991 Numerator of Hermite(n, 4/7).

1, 8, -34, -1840, -4724, 683488, 7782664, -339629632, -8055944560, 201822075008, 8719919701984, -128026275891968, -10424283645874496, 67164631281958400, 13817854415099775104, 18392961201951276032, -20165102300581059194624, -190160981569308074375168

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Examples

			Numerator of 1, 8/7, -34/49, -1840/343, -4724/2401, 683488/16807, 7782664/117649...
		

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)*(8/7)^(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

A158991 := proc(n)
        orthopoly[H](n,4/7) ;
        numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014

Mathematica

Numerator[Table[HermiteH[n,4/7],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Mar 23 2011*)
Table[7^n*HermiteH[n, 4/7], {n,0,30}] (* G. C. Greubel, Jul 09 2018 *)

PARI

a(n)=numerator(polhermite(n,4/7)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

D-finite with recurrence a(n) -8*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, 4/7).

E.g.f.: exp(8*x - 49*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(8/7)^(n-2*k)/(k!*(n-2*k)!)). (End)