

A262856


Numerators of the NielsenJacobsthal series leading to Euler's constant.


4




OFFSET

1,2


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. 365396, 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

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


MATHEMATICA

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


PROG

(PARI) a(n) = numerator(n*sum(k=2^n + 1, 2^(n + 1), (1)^(k + 1)/k));
(MAGMA) [Numerator(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)), NumeratorRat); # Muniru A Asiru, Oct 29 2018


CROSSREFS

Cf. A075266, A075267, A001620, A195189, A002657, A002790, A262235, A075266, A006953, A001067, A262858 (denominators of this series).
Sequence in context: A147522 A183489 A184144 * A302484 A177488 A262648
Adjacent sequences: A262853 A262854 A262855 * A262857 A262858 A262859


KEYWORD

frac,nonn


AUTHOR

Iaroslav V. Blagouchine, Oct 03 2015


STATUS

approved



