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A238181
Decimal expansion of sum_(n>=1) H(n)^2/n^3 where H(n) is the n-th harmonic number (Quadratic Euler Sum S(2,3)).
11
1, 6, 5, 1, 9, 4, 2, 7, 9, 2, 7, 0, 4, 4, 9, 8, 6, 2, 3, 9, 6, 2, 6, 9, 3, 7, 6, 1, 1, 1, 4, 4, 9, 4, 0, 1, 6, 1, 1, 7, 6, 3, 1, 7, 5, 1, 5, 9, 6, 5, 6, 0, 6, 3, 3, 2, 1, 3, 8, 5, 2, 0, 9, 5, 6, 0, 8, 5, 9, 7, 5, 3, 0, 1, 0, 5, 3, 8, 0, 9, 8, 8, 2, 5, 7, 7, 6, 6, 5, 0, 0, 4, 2, 8, 2, 1, 7, 0, 6, 9
OFFSET
1,2
LINKS
Philippe Flajolet, Bruno Salvy, Euler Sums and Contour Integral Representations, Experimental Mathematics 7:1 (1998) page 24.
FORMULA
7/2*zeta(5) - zeta(2)*zeta(3).
EXAMPLE
1.6519427927044986239626937611144940161...
MATHEMATICA
7/2*Zeta[5] - Zeta[2]*Zeta[3] // RealDigits[#, 10, 100]& // First
PROG
(PARI) 7/2*zeta(5) - zeta(2)*zeta(3) \\ Stefano Spezia, May 22 2025
KEYWORD
nonn,cons
AUTHOR
STATUS
approved