login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A159807 Numerator of Hermite(n, 3/22). 1
1, 3, -233, -2151, 162705, 2570283, -189162201, -4299537519, 307542155937, 9246531104595, -642087222317001, -24302866940070903, 1636327584987643953, 75484508348928834171, -4921433057324341373625, -270505813458143914292223, 17053284557712927443382081 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..435

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

FORMULA

From Vincenzo Librandi, Jan 20 2017: (Start)

Conjecture: E.g.f.: exp(-x*(121*x-3)).

D-finite with recurrence a(n) = 3*a(n-1) - 242*(n-1)*a(n-2). [DLMF] Corrected Feb 06 2021 (End)

EXAMPLE

Numerators of 1, 3/11, -233/121, -2151/1331, 162705/14641, ...

MATHEMATICA

Numerator/@HermiteH[Range[0, 20], 3/22]  (* Harvey P. Dale, May 01 2011 *)

PROG

(PARI) a(n)=numerator(polhermite(n, 3/22)) \\ Charles R Greathouse IV, Jan 29 2016

(Sage) [numerator(hermite(n, 3/22)) for n in range(20)] # Bruno Berselli, Jan 19 2017

(Maxima) makelist(num(hermite(n, 3/22)), n, 0, 20); /* Bruno Berselli, Jan 19 2017 */

(MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(3/11)^(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 *)

CROSSREFS

Cf. A001020 (denominators).

Sequence in context: A099426 A332123 A100201 * A065580 A072320 A162603

Adjacent sequences:  A159804 A159805 A159806 * A159808 A159809 A159810

KEYWORD

sign,frac

AUTHOR

N. J. A. Sloane, Nov 12 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 30 03:59 EDT 2021. Contains 346348 sequences. (Running on oeis4.)