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 A242612 Decimal expansion of the sum of the alternating series tau(4), with tau(n) = Sum_{k>0} (-1)^k*log(k)^n/k. 3
 0, 1, 7, 9, 9, 6, 9, 3, 8, 1, 0, 6, 8, 9, 1, 4, 0, 7, 7, 9, 5, 3, 6, 7, 8, 2, 1, 4, 3, 6, 1, 5, 2, 6, 2, 3, 8, 9, 8, 1, 1, 2, 3, 4, 5, 1, 3, 9, 0, 2, 3, 3, 4, 9, 2, 9, 4, 5, 0, 2, 4, 7, 9, 9, 9, 1, 3, 2, 2, 5, 6, 2, 4, 6, 3, 8, 0, 8, 5, 8, 4, 3, 0, 9, 4, 2, 9, 7, 0, 5, 9, 1, 9, 5, 1, 4, 2, 4, 2, 9, 9 (list; constant; graph; refs; listen; history; text; internal format)
 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 Cf. A001620, A082633, A086279, A086280, A242494, A242611, A242613. Sequence in context: A198753 A244625 A175642 * A199386 A143959 A121313 Adjacent sequences:  A242609 A242610 A242611 * A242613 A242614 A242615 KEYWORD nonn,cons AUTHOR Jean-François Alcover, May 19 2014 STATUS approved

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Last modified January 21 05:39 EST 2020. Contains 331104 sequences. (Running on oeis4.)