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A075266
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Numerator of the coefficient of x^n in log(-log(1-x)/x).
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16
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1, 5, 1, 251, 19, 19087, 751, 1070017, 2857, 26842253, 434293, 703604254357, 8181904909, 1166309819657, 5044289, 8092989203533249, 5026792806787, 12600467236042756559, 69028763155644023, 8136836498467582599787
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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MAPLE
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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:
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MATHEMATICA
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Numerator[ CoefficientList[ Series[ Log[ -Log[1 - x]/x], {x, 0, 20}], x]]
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CROSSREFS
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KEYWORD
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frac,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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