A241215 Decimal expansion of sum_(n>=1) H(n)^4/(n+1)^3 where H(n) is the n-th harmonic number.

1, 8, 0, 1, 6, 1, 3, 2, 6, 8, 0, 4, 3, 4, 1, 2, 9, 0, 3, 7, 2, 9, 4, 8, 8, 9, 4, 2, 0, 2, 0, 8, 8, 8, 4, 3, 0, 3, 1, 3, 7, 7, 5, 8, 2, 7, 7, 8, 7, 8, 9, 3, 3, 0, 0, 8, 7, 3, 3, 9, 4, 9, 2, 5, 4, 8, 0, 4, 4, 4, 8, 1, 8, 8, 4, 0, 8, 9, 3, 3, 3, 7, 5, 3, 0, 9, 4, 5, 7, 4, 3, 3, 0, 4, 2, 7, 1, 9, 3, 1

Offset

1,2

Links

Table of n, a(n) for n=1..100.

Philippe Flajolet, Bruno Salvy, Euler Sums and Contour Integral Representations, Experimental Mathematics 7:1 (1998) page 16.

Formula

37/2*zeta(3)*zeta(4) - 5*zeta(2)*zeta(5) - 109/8*zeta(7)

= 37/180*Pi^4*zeta(3) - 5/6*Pi^2*zeta(5) - 109/8*zeta(7)

Example

1.80161326804341290372948894202088843...

Mathematica

37/180*Pi^4*Zeta[3] - 5/6*Pi^2*Zeta[5] - 109/8*Zeta[7] // RealDigits[#, 10, 100]& // First

Crossrefs

Cf. A016627, A083680, A102886, A152648, A152649, A152651, A233033, A233090, A238166, A238167, A239168, A238169, A238181, A238182, A238183, A240264.

Sequence in context: A198940 A321107 A198117 * A272343 A011314 A021559

Adjacent sequences: A241212 A241213 A241214 * A241216 A241217 A241218

Keyword

nonn,cons

Author

Jean-François Alcover, Apr 17 2014

Status

approved