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A247450 Decimal expansion of c(4), a constant appearing in certain Euler double sums not expressible in terms of well-known constants. 1
2, 1, 1, 7, 1, 4, 1, 7, 3, 4, 7, 7, 7, 0, 3, 9, 4, 1, 1, 1, 2, 9, 1, 0, 0, 2, 2, 6, 0, 1, 2, 4, 5, 1, 7, 5, 1, 9, 1, 7, 6, 8, 0, 7, 6, 6, 9, 1, 6, 0, 8, 4, 0, 6, 9, 3, 6, 7, 6, 6, 3, 9, 0, 2, 7, 0, 4, 9, 4, 8, 2, 1, 2, 9, 8, 0, 6, 7, 5, 0, 9, 4, 9, 6, 0, 3, 6, 2, 6, 6, 0, 6, 8, 7, 7, 9, 0, 4, 6, 6, 3, 4, 5, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..104.

J. M. Borwein, I.J. Zucker and J. Boersma, The evaluation of character Euler double sums, The Ramanujan Journal, April 2008, Volume 15, Issue 3, pp 377-405, see p. 17 c(4).

FORMULA

c(n) = sum_{k=0..n-2} (n-2)!/k!*log(2)^k*Li_(n-k)(1/2) + log(2)^n/n.

c(4) = (1/12)*((-Pi^2)*log(2)^2 + log(2)^4 + 24*Li_4(1/2) + 21*log(2)*zeta(3)).

EXAMPLE

2.117141734777039411129100226012451751917680766916084...

MATHEMATICA

c[4] = (1/12)*((-Pi^2)*Log[2]^2 + Log[2]^4 + 24*PolyLog[4, 1/2] + 21*Log[2]*Zeta[3]); RealDigits[c[4], 10, 104] // First

CROSSREFS

Cf. A002162 c(1), A072691 c(2), A233091 c(3).

Sequence in context: A214631 A025270 A249450 * A178234 A259175 A297431

Adjacent sequences:  A247447 A247448 A247449 * A247451 A247452 A247453

KEYWORD

nonn,cons,easy

AUTHOR

Jean-Fran├žois Alcover, Sep 17 2014

STATUS

approved

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Last modified February 20 17:04 EST 2020. Contains 332080 sequences. (Running on oeis4.)