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!)
A160071 Numerator of Hermite(n, 5/26). 1
1, 5, -313, -4945, 292657, 8148925, -453845705, -18795248425, 979822695905, 55721465220725, -2702013314839385, -201848619020247425, 9036842409471596305, 863882210793481537325, -35388474493250786477545, -4264832993941008567009625, 158095400711076444606105025 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..422

FORMULA

From G. C. Greubel, Sep 23 2018: (Start)

a(n) = 13^n * Hermite(n, 5/26).

E.g.f.: exp(5*x - 169*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(5/13)^(n-2*k)/(k!*(n-2*k)!)). (End)

EXAMPLE

Numerators of 1, 5/13, -313/169, -4945/2197, 292657/28561, ...

MATHEMATICA

Table[13^n*HermiteH[n, 5/26], {n, 0, 30}] (* G. C. Greubel, Sep 23 2018 *)

PROG

(PARI) a(n)=numerator(polhermite(n, 5/26)) \\ Charles R Greathouse IV, Jan 29 2016

(PARI) x='x+O('x^30); Vec(serlaplace(exp(5*x - 169*x^2))) \\ G. C. Greubel, Sep 23 2018

(MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(5/13)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 23 2018

CROSSREFS

Cf. A001022 (denominators).

Sequence in context: A300610 A301352 A075983 * A094161 A130308 A304212

Adjacent sequences:  A160068 A160069 A160070 * A160072 A160073 A160074

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 August 2 18:31 EDT 2021. Contains 346428 sequences. (Running on oeis4.)