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%I #15 Mar 16 2021 04:07:29
%S 7,4,3,9,7,1,1,9,3,3,5,0,3,7,4,7,4,4,6,8,6,5,5,9,6,0,7,5,8,5,6,5,0,0,
%T 0,0,9,8,6,0,0,8,6,9,2,8,6,1,3,2,7,8,7,3,3,1,9,5,1,2,3,8,9,1,7,2,2,4,
%U 6,7,4,3,0,5,6,9,7,9,5,3,4,0,6,2,5,2,3,6,2,1,8,1,8,7,1,7,2,5
%N Decimal expansion of constant 5 * Pi^2 * A065476 / 48.
%H G. Niklasch, <a href="/A001692/a001692.html">Some number theoretical constants: 1000-digit values</a>. [Cached copy]
%e 0.743971193350374744686559607585650...
%t $MaxExtraPrecision = 500; digits = 98; terms = 500; P[n_] := PrimeZetaP[n] - 1/2^n; LR = Join[{0, 0}, LinearRecurrence[{0, 1, 2}, {-2, -6, -2}, terms + 10]]; r[n_Integer] := LR[[n]]; (5 Pi^2/48)*Exp[NSum[r[n]*P[n - 1]/(n - 1), {n, 3, terms}, NSumTerms -> terms, WorkingPrecision -> digits + 10]] // RealDigits[#, 10, digits]& // First (* _Jean-François Alcover_, Apr 18 2016 *)
%o (PARI) (5 * Pi^2 / 48) * prodeulerrat(1 - (p+2)/p^3, 1, 3) \\ _Amiram Eldar_, Mar 16 2021
%Y Cf. A065476, A078088.
%K cons,nonn
%O 0,1
%A _N. J. A. Sloane_, Nov 19 2001
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