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A238182
Decimal expansion of Sum_{n>=1} H(n)^2/n^4 where H(n) is the n-th harmonic number (Quadratic Euler Sum S(2,4)).
3
1, 2, 2, 1, 8, 7, 9, 9, 4, 5, 3, 1, 9, 8, 8, 0, 1, 3, 8, 5, 1, 8, 8, 0, 6, 4, 7, 5, 2, 9, 0, 9, 9, 4, 8, 1, 2, 5, 6, 9, 0, 4, 1, 5, 4, 4, 0, 2, 1, 6, 7, 2, 4, 6, 4, 1, 8, 3, 5, 3, 3, 3, 5, 9, 8, 8, 7, 0, 0, 8, 1, 9, 3, 6, 3, 2, 7, 0, 4, 9, 6, 6, 6, 7, 7, 1, 5, 8, 6, 3, 0, 4, 6, 4, 5, 4, 4, 6, 8, 6
OFFSET
1,2
COMMENTS
No closed form of S(2,2q) is known to date, except for S(2,2) (A218505) and S(2,4) (this sequence).
LINKS
Philippe Flajolet, Bruno Salvy, Euler Sums and Contour Integral Representations, Experimental Mathematics 7:1 (1998) page 24.
FORMULA
97/24*zeta(6) - 2*zeta(3)^2.
EXAMPLE
1.221879945319880138518806475290994812569...
MATHEMATICA
97/24*Zeta[6] - 2*Zeta[3]^2 // RealDigits[#, 10, 100]& // First
KEYWORD
nonn,cons
AUTHOR
STATUS
approved