A247450 Decimal expansion of c(4), a constant appearing in certain Euler double sums not expressible in terms of well-known constants.

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

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: A249450 A373343 A331501 * A178234 A344440 A259175

Adjacent sequences: A247447 A247448 A247449 * A247451 A247452 A247453

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Sep 17 2014

Status

approved