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A244667
Decimal expansion of sum_(n>=1) (H(n)^3/(n+1)^2) where H(n) is the n-th harmonic number.
7
9, 7, 5, 4, 2, 6, 2, 5, 1, 3, 8, 7, 2, 5, 7, 0, 5, 6, 5, 6, 8, 2, 3, 2, 6, 5, 8, 9, 9, 1, 2, 8, 8, 1, 8, 3, 2, 5, 1, 0, 2, 5, 8, 3, 6, 2, 9, 2, 4, 4, 8, 0, 2, 9, 8, 5, 0, 2, 2, 6, 7, 3, 6, 1, 3, 3, 3, 2, 4, 1, 9, 5, 7, 5, 4, 3, 7, 1, 5, 3, 4, 1, 9, 0, 2, 7, 0, 7, 6, 7, 1, 7, 0, 0, 2, 4, 9, 6, 3, 0, 2
OFFSET
1,1
LINKS
Philippe Flajolet, Bruno Salvy, Euler Sums and Contour Integral Representations, Experimental Mathematics 7:1 (1998) page 27.
FORMULA
Equals Pi^2/6*zeta(3) + 15/2*zeta(5).
EXAMPLE
9.75426251387257056568232658991288183251025836292448029850226736133324...
MATHEMATICA
RealDigits[15/2*Zeta[5] + Zeta[2]*Zeta[3], 10, 101] // First
PROG
(PARI) default(realprecision, 100); Pi^2/6*zeta(3) + 15/2*zeta(5) \\ G. C. Greubel, Aug 31 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); L:=RiemannZeta(); Pi(R)^2/6*Evaluate(L, 3) + 15/2*Evaluate(L, 5); // G. C. Greubel, Aug 31 2018
CROSSREFS
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved