A211163 Numerator of (-1/Pi^n) * integral_{0..1} (log(1-1/x)^n) dx.

2, 0, 8, 0, 32, 0, 128, 0, 2560, 0, 1415168, 0, 57344, 0, 118521856, 0, 5749735424, 0, 91546451968, 0, 1792043646976, 0, 1982765704675328, 0, 286994513002496, 0, 3187598700536922112, 0, 4625594563496048066560

Offset: 2

Author

Jean-François Alcover, Jan 30 2013

Keywords

• nonn
• frac

Comments

Conjecture: sequence of denominators is A141459.

Examples

			2*Pi^2/3, 0, 8*Pi^4/15, 0, 32*Pi^6/21, 0, 128*Pi^8/15, 0, 2560*Pi^10/33, ...
		

Crossrefs

Cf. A079484 (Gerry Martens's Pari program uses this integral).

Programs

Mathematica

a[n_] := (-1/Pi^n)*Numerator[Integrate[Log[1 - 1/x]^n, {x, 0, 1}]]; Table[Print[an = a[n]]; an, {n, 2, 30}]