OFFSET
0,3
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, chapter 2.21, p. 168.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..10000
FORMULA
tau(n) = -log(2)^(n+1)/(n+1) + Sum_(k=0..n-1) (binomial(n, k)*log(2)^(n-k)*gamma(k)).
tau(4) = gamma*log(2)^4 - (1/5)*log(2)^5 + 4*log(2)^3*gamma(1) + 6*log(2)^2*gamma(2) + 4*log(2)*gamma(3).
EXAMPLE
-0.017996938106891407795367821436152623898...
MATHEMATICA
tau[n_] := -Log[2]^(n+1)/(n+1) + Sum[Binomial[n, k]*Log[2]^(n-k)*StieltjesGamma[k], {k, 0, n-1}]; Join[{0}, RealDigits[tau[4], 10, 100] // First]
PROG
(PARI) sumalt(k=1, (-1)^k*log(k)^4/k) \\ Charles R Greathouse IV, Mar 10 2016
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, May 19 2014
STATUS
approved