A241215 - OEIS

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

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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