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

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A160313 Numerator of Hermite(n, 15/31). 1
1, 30, -1022, -145980, 1513452, 1167697800, 20486660280, -12851291221200, -661166264043120, 177766465895877600, 16769848012294217760, -2913576034149940939200, -441955407700422580057920, 53940055420621560419971200, 12660899479421405397926325120 (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, 15/31).

a(n+2) = 30*a(n+1) - 1922*(n+1)*a(n)

E.g.f.: exp(30*x - 961*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(30/31)^(n-2*k)/(k!*(n-2*k)!)). (End)

EXAMPLE

Numerators of 1, 30/31, -1022/961, -145980/29791, 1513452/923521, ...

MATHEMATICA

Table[31^n*HermiteH[n, 15/31], {n, 0, 30}] (* G. C. Greubel, Oct 04 2018 *)

PROG

(PARI) a(n)=numerator(polhermite(n, 15/31)) \\ Charles R Greathouse IV, Jan 29 2016

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

(MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(30/31)^(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: A061466 A180812 A292002 * A001821 A027488 A269541

Adjacent sequences:  A160310 A160311 A160312 * A160314 A160315 A160316

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 December 6 04:20 EST 2021. Contains 349562 sequences. (Running on oeis4.)