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A241215 Decimal expansion of sum_(n>=1) H(n)^4/(n+1)^3 where H(n) is the n-th harmonic number. 0
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 (list; constant; graph; refs; listen; history; text; internal format)
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: A011470 A198940 A198117 * A272343 A011314 A021559

Adjacent sequences:  A241212 A241213 A241214 * A241216 A241217 A241218

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, Apr 17 2014

STATUS

approved

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Last modified June 24 13:17 EDT 2019. Contains 324325 sequences. (Running on oeis4.)