A075266 Numerator of the coefficient of x^n in log(-log(1-x)/x).

1, 5, 1, 251, 19, 19087, 751, 1070017, 2857, 26842253, 434293, 703604254357, 8181904909, 1166309819657, 5044289, 8092989203533249, 5026792806787, 12600467236042756559, 69028763155644023, 8136836498467582599787

Offset

1,2

Comments

A series with these numerators leads to Euler's constant: gamma = 1 - 1/4 - 5/72 - 1/32 - 251/14400 - 19/1728 - 19087/2540160 - ..., see references [Blagouchine] below, as well as A262235. - Iaroslav V. Blagouchine, Sep 15 2015

Links

Robert Israel, Table of n, a(n) for n = 1..447

Iaroslav V. Blagouchine, Two series expansions for the logarithm of the gamma function involving Stirling numbers and containing only rational coefficients for certain arguments related to 1/pi, Journal of Mathematical Analysis and Applications (Elsevier), 2016. arXiv version, arXiv:1408.3902 [math.NT], 2014-2016

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.

Maple

S:= series(log(-log(1-x)/x), x, 51):
seq(numer(coeff(S, x, j)), j=1..50); # Robert Israel, May 17 2016
# Alternative:
a := proc(n) local r; r := proc(n) option remember; if n=0 then 1 else
1 - add(r(k)/(n-k+1), k=0..n-1) fi end: numer(r(n)/(n*(n+1))) end:
seq(a(n), n=1..20); # Peter Luschny, Apr 19 2018

Mathematica

Numerator[ CoefficientList[ Series[ Log[ -Log[1 - x]/x], {x, 0, 20}], x]]

Crossrefs

Cf. A053657, A075264, A075267, A262235.

Sequence in context: A294257 A360989 A162227 * A094096 A009826 A255855

Adjacent sequences: A075263 A075264 A075265 * A075267 A075268 A075269

Keyword

frac,nonn

Author

Paul D. Hanna, Sep 15 2002

Extensions

Edited by Robert G. Wilson v, Sep 17 2002

Status

approved