A262858 Denominators of the Nielsen-Jacobsthal series leading to Euler's constant.

12, 420, 240240, 36100888223400, 236453376820564453502272320, 2225626015166235263233958200740039423756478781341512000

Offset

1,1

Comments

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

Links

G. C. Greubel, Table of n, a(n) for n = 1..10

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));
(Magma) [Denominator(n*(&+[(-1)^(k+1)/k: k in [2^n+1..2^(n+1)]])): n in [1..6]];  // G. C. Greubel, Oct 28 2018
(GAP) List(List([1..6], n->n*Sum([2^n+1..2^(n+1)], k->(-1)^(k+1)/k)), DenominatorRat); # Muniru A Asiru, Oct 29 2018

Crossrefs

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

Sequence in context: A098602 A000897 A036687 * A123778 A347795 A129006

Adjacent sequences: A262855 A262856 A262857 * A262859 A262860 A262861

Keyword

frac,nonn

Author

Iaroslav V. Blagouchine, Oct 03 2015

Status

approved