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

0,2

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)

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)

Example

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

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 *)

Prog

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

Crossrefs

Cf. A000420 (denominators)

Sequence in context: A203445 A318244 A280395 * A265161 A303805 A360658

Adjacent sequences: A158988 A158989 A158990 * A158992 A158993 A158994

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved