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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A262858 Denominators of the Nielsen-Jacobsthal series leading to Euler's constant. 3
12, 420, 240240, 36100888223400, 236453376820564453502272320, 2225626015166235263233958200740039423756478781341512000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

gamma = 1 - 1/12 - 43/420 - 20431/240240 - 2150797323119/36100888223400 - ..., see formula (36) in the reference below.

LINKS

Table of n, a(n) for n=1..6.

Iaroslav V. Blagouchine, Expansions of generalized Euler's constants into the series of polynomials in 1/pi^2 and into the formal enveloping series with rational coefficients only. Journal of Number Theory (Elsevier), vol. 158, pp. 365-396, 2016. arXiv version, arXiv:1501.00740 [math.NT], 2015.

FORMULA

a(n) = n * Sum_{k = 2^n + 1 .. 2^(n + 1)} (-1)^(k + 1)/k.

EXAMPLE

Denominators of 1/12, 43/420, 20431/240240, 2150797323119/36100888223400, ...

MATHEMATICA

a[n_] := Denominator[n*Sum[(-1)^(k + 1)/k, {k, 2^n + 1, 2^(n + 1)}]]; Table[a[n], {n, 1, 8}]

PROG

(PARI) a(n) = denominator(n*sum(k=2^n + 1, 2^(n + 1), (-1)^(k + 1)/k));

CROSSREFS

Cf. A075266, A075267, A001620, A195189, A002657, A002790, A262235, A075266, A006953, A001067, A262856 (numerators of this series).

Sequence in context: A098602 A000897 A036687 * A123778 A129006 A067429

Adjacent sequences:  A262855 A262856 A262857 * A262859 A262860 A262861

KEYWORD

frac,nonn

AUTHOR

Iaroslav V. Blagouchine, Oct 03 2015

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 October 22 16:41 EDT 2018. Contains 316490 sequences. (Running on oeis4.)