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A238169
Decimal expansion of sum_(n>=1) H(n)^3/n^4 where H(n) is the n-th harmonic number.
5
1, 3, 8, 1, 4, 6, 8, 3, 1, 0, 5, 0, 3, 8, 5, 2, 3, 7, 3, 0, 0, 4, 7, 8, 5, 1, 2, 0, 4, 0, 6, 6, 2, 2, 6, 9, 9, 9, 3, 3, 4, 4, 3, 5, 6, 3, 9, 0, 5, 3, 6, 1, 6, 9, 1, 0, 0, 0, 0, 8, 5, 3, 3, 0, 9, 5, 3, 8, 7, 2, 4, 2, 2, 3, 7, 7, 7, 5, 8, 4, 6, 7, 2, 9, 5, 9, 9, 3, 2, 6, 4, 5, 0, 9, 3, 0, 5, 7, 4, 1
OFFSET
1,2
LINKS
Philippe Flajolet, Bruno Salvy, Euler Sums and Contour Integral Representations, Experimental Mathematics 7:1 (1998) page 16.
FORMULA
Equals (231/16)*Zeta(7) - (51/4)*Zeta(3)*Zeta(4) + 2*Zeta(2)*Zeta(5).
EXAMPLE
1.38146831050385237300478512040662269993...
MATHEMATICA
RealDigits[(231/16)*Zeta[7] - (51/4)*Zeta[3]*Zeta[4] + 2*Zeta[2]*Zeta[5], 10, 100][[1]] (* G. C. Greubel, Dec 30 2017 *)
PROG
(PARI) (231/16)*zeta(7) - (51/4)*zeta(3)*zeta(4) + 2*zeta(2)*zeta(5) \\ G. C. Greubel, Dec 30 2017
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
STATUS
approved