A160445 Numerator of Hermite(n, 20/21).

1, 40, 718, -41840, -3573428, 4674400, 15945793480, 613094814400, -73925536369520, -7283018465187200, 295500169093761760, 76056229626701574400, 175306544520386380480, -797966872588194008230400, -33928739742998510567799680, 8496145352999079190916992000

Offset

0,2

Links

Table of n, a(n) for n=0..15.

DLMF Digital library of mathematical functions, Table 18.9.1 for H_n(x)

Formula

E.g.f.: exp(-x*(441*x-40)). - Vincenzo Librandi, Jan 20 2017

D-finite with recurrence a(n) = 40*a(n-1)-882*(n-1)*a(n-2). - [DLMF] Vincenzo Librandi, Jan 20 2017, corrected Feb 06 2021

Example

Numerators of 1, 40/21, 718/441, -41840/9261, -3573428/194481, ...

Mathematica

HermiteH[Range[0, 20], 20/21]//Numerator (* Harvey P. Dale, Dec 05 2022 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 20/21)) \\ Charles R Greathouse IV, Jan 29 2016

Crossrefs

Cf. A009965 (denominators).

Sequence in context: A183464 A359932 A189286 * A010840 A233725 A175603

Adjacent sequences: A160442 A160443 A160444 * A160446 A160447 A160448

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved