login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A160315 Numerator of Hermite(n, 17/31). 1
1, 34, -766, -156740, -912404, 1173995384, 48684045496, -11883257221424, -1059025893631600, 146710082653141024, 23307172718246211616, -2027323916172999286336, -561689258759043381720896, 27660764004806580561543040, 14974833795516881674770770816 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..368

FORMULA

From G. C. Greubel, Oct 04 2018: (Start)

a(n) = 31^n * Hermite(n, 17/31).

a(n+2) = 34*a(n+1) - 1922*(n+1)*a(n)

E.g.f.: exp(34*x - 961*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(34/31)^(n-2*k)/(k!*(n-2*k)!)). (End)

EXAMPLE

Numerators of 1, 34/31, -766/961, -156740/29791, -912404/923521, ...

MATHEMATICA

Numerator[HermiteH[Range[0, 20], 17/31]] (* Harvey P. Dale, Feb 24 2013 *)

Table[31^n*HermiteH[n, 17/31], {n, 0, 30}] (* G. C. Greubel, Oct 04 2018 *)

PROG

(PARI) a(n)=numerator(polhermite(n, 17/31)) \\ Charles R Greathouse IV, Jan 29 2016

(PARI) x='x+O('x^30); Vec(serlaplace(exp(34*x - 961*x^2))) \\ G. C. Greubel, Oct 04 2018

(MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(34/31)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 04 2018

CROSSREFS

Cf. A009975 (denominators).

Sequence in context: A295378 A028023 A025190 * A078193 A063843 A192094

Adjacent sequences:  A160312 A160313 A160314 * A160316 A160317 A160318

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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 24 07:57 EDT 2022. Contains 354005 sequences. (Running on oeis4.)