A340485 Decimal expansion of Sum_{k>=2} log(k)/(k^2-1)^2.
1, 0, 7, 3, 2, 5, 3, 7, 1, 6, 4, 2, 0, 3, 0, 2, 3, 9, 6, 9, 5, 0, 6, 0, 2, 4, 8, 5, 0, 2, 1, 8, 2, 8, 8, 0, 3, 2, 4, 7, 2, 7, 9, 8, 9, 8, 2, 0, 4, 3, 6, 1, 5, 7, 4, 8, 7, 9, 3, 3, 8, 9, 2, 4, 6, 9, 8, 2, 7, 9, 9, 0, 2, 0, 8, 7, 4, 8, 6, 9, 4, 5, 1, 6, 8, 5, 3, 4, 3, 9, 9, 1, 9, 9, 3, 2, 6, 1, 2, 5, 3, 9, 7, 1, 0, 7
Offset: 0
Examples
0.10732537164203023969506024850218288032472798982043615...
Programs
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Maple
evalf(-Zeta'(4) - Sum(i * Zeta'(2*i+2), i = 2 .. infinity), 120); # Amiram Eldar, Mar 09 2024
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PARI
sumpos(k=2, log(k)/(k^2-1)^2) \\ Michel Marcus, Jan 09 2021
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PARI
-zeta'(4) - sumpos(i=2, i*zeta'(2*i+2)) \\ Amiram Eldar, Mar 09 2024
Formula
Equals -Sum_{i>=1} i*zeta'(2*i+2) = A261506 - Sum_{i>=2} i*zeta'(2*i+2).
Extensions
More terms from Amiram Eldar, Mar 09 2024