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A242613 Decimal expansion of the sum of the alternating series tau(5), with tau(n) = Sum_{k>0} (-1)^k*log(k)^n/k. 3
0, 2, 4, 5, 1, 4, 9, 0, 7, 6, 5, 6, 4, 0, 9, 7, 8, 2, 9, 0, 7, 4, 2, 2, 8, 0, 0, 6, 8, 6, 1, 3, 7, 1, 1, 0, 2, 8, 7, 5, 7, 0, 7, 0, 9, 2, 3, 7, 9, 1, 5, 0, 3, 7, 4, 2, 9, 0, 5, 1, 1, 2, 7, 2, 9, 8, 3, 7, 8, 8, 0, 0, 9, 9, 7, 5, 5, 3, 3, 5, 8, 9, 1, 5, 4, 6, 6, 2, 9, 4, 6, 0, 6, 2, 9, 3, 7, 4, 1, 7, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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(5) = gamma*log(2)^5 - (1/6)*log(2)^6 + 5*log(2)^4*gamma(1) + 10*log(2)^3*gamma(2) + 10*log(2)^2*gamma(3) + 5*log(2)*gamma(4).

EXAMPLE

-0.02451490765640978290742280068613711...

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[5], 10, 100] // First]

CROSSREFS

Cf. A001620, A082633, A086279, A086280, A086281, A242494, A242611, A242612.

Sequence in context: A225153 A308319 A167380 * A196548 A274316 A075884

Adjacent sequences:  A242610 A242611 A242612 * A242614 A242615 A242616

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, May 19 2014

STATUS

approved

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Last modified November 21 14:18 EST 2019. Contains 329371 sequences. (Running on oeis4.)