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A238166
Decimal expansion of sum_(n>=1) H(n,2)/n^4 where H(n,2) = A007406(n)/A007407(n) is the n-th harmonic number of order 2.
5
1, 1, 0, 5, 8, 2, 6, 4, 4, 4, 4, 3, 8, 8, 1, 7, 8, 5, 4, 0, 0, 8, 8, 4, 5, 7, 6, 8, 8, 7, 6, 6, 8, 0, 9, 8, 4, 5, 4, 9, 7, 9, 6, 2, 4, 2, 4, 1, 9, 6, 0, 4, 1, 5, 3, 5, 1, 7, 2, 9, 7, 9, 4, 0, 5, 6, 3, 8, 0, 6, 4, 6, 1, 8, 3, 0, 7, 0, 1, 4, 6, 9, 3, 3, 8, 6, 0, 1, 7, 7, 2, 5, 3, 9, 0, 0, 5, 7, 5, 7
OFFSET
1,4
LINKS
Philippe Flajolet, Bruno Salvy, Euler Sums and Contour Integral Representations, Experimental Mathematics 7:1 (1998) page 16.
FORMULA
Equals zeta(3)^2 - zeta(6)/3.
EXAMPLE
1.1058264444388178540088457688766809845497962424196...
MATHEMATICA
RealDigits[Zeta[3]^2 - 1/3*Zeta[6], 10, 100][[1]]
PROG
(PARI) zeta(3)^2-Pi^6/2835 /* Michel Marcus, Jul 04 2014 */
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved