login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A145609 Numerator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=1. 41
3, 25, 49, 761, 7381, 86021, 1171733, 2436559, 14274301, 55835135, 19093197, 1347822955, 34395742267, 315404588903, 9304682830147, 586061125622639, 54062195834749, 54801925434709, 2053580969474233, 2078178381193813 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The polynomials A_{2n+1}(x) = sum_{d=1..2n} x^(2n+1-d)/d for small n look as follows:

n=1, index = 3: A_3(x) = x/2 + x^2.

n=2, index = 5: A_5(x) = x/4 + x^2/3 + x^3/2 + x^4.

n=3, index = 7: A_7(x) = x/6 + x^2/5 + x^3/4 + x^4/3 + x^5/2 + x^6.

n=4, index = 9: A_9(x) = x/8 + x^2/7 + x^3/6 + x^4/5 + x^5/4 + x^6/3 + x^7/2 + x^8.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

FORMULA

(1/(2*n+1))*2F1(1, 2*n+1; 2*n+2; 1/m) = Sum_{x>=0} m^(-x)/(x+2n+1) = m^(2n)*arctanh((2m-1)/(2m^2-2m+1)) - A_{2n+1}(m) = m^(2n)*log(m/(m-1)) - A_{2n+1}(m). - Artur Jasinski, Oct 14 2008

It appears that A145609(n)/A145610(n) = H(2*n+2), the harmonic number of order 2*n+2. - Groux Roland, Jan 08 2011

Yes, A145609(n)/A145610(n) = H(2*n+2), as A_l(x) = sum_{d=1..l-1} x^(l-d)/d at x=1 is just sum_{d=1..l-1}1/d = H(l-1), the harmonic number of order (l-1). - Zak Seidov, Jan 09 2014

a(n) = numerator of Integral_{x=0..1} ((1 - x^(2*n))/(1 - x). - Peter Luschny, Sep 28 2017

MAPLE

A := proc(l, x) add(x^(l-d)/d, d=1..l-1) ; end: A145609 := proc(n) numer( A(2*n+1, 1)) ; end: seq(A145609(n), n=1..20) ; # R. J. Mathar, Aug 21 2009

MATHEMATICA

m = 1; aa = {}; Do[k = 0; Do[k = k + m^(2 r + 1 - d)/d, {d, 1, 2 r}]; AppendTo[aa, Numerator[k]], {r, 1, 25}]; aa (* Artur Jasinski *)

CROSSREFS

For denominators see A145610.

Cf. A145611-A145640.

Sequence in context: A266702 A264937 A051280 * A259923 A120285 A041897

Adjacent sequences:  A145606 A145607 A145608 * A145610 A145611 A145612

KEYWORD

frac,nonn

AUTHOR

Artur Jasinski, Oct 14 2008

EXTENSIONS

Edited, parentheses in front of Gauss. Hypg. Fct. added by R. J. Mathar, Aug 21 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 25 06:31 EST 2018. Contains 299643 sequences. (Running on oeis4.)