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%I #21 Mar 20 2017 23:11:22
%S 8,6,9,0,0,1,9,9,1,9,6,2,9,0,8,9,9,8,8,1,1,0,5,4,8,0,5,5,6,1,3,9,5,6,
%T 8,8,8,9,2,4,9,4,8,4,1,8,8,0,5,7,7,8,5,0,7,1,0,6,4,5,7,7,8,5,6,0,6,7,
%U 4,6,0,9,5,5,4,2,5,8,0,1,3,5,8,7,6,7,1,9,6,4,5,9,3,3,5,3,8,1,1,8,0,9
%N Decimal expansion of Sum_{n>=1} zeta(2n)/(2n)!.
%H G. C. Greubel, <a href="/A093721/b093721.txt">Table of n, a(n) for n = 0..10000</a>
%H J. Sondow and E. W. Weisstein, <a href="http://mathworld.wolfram.com/RiemannZetaFunction.html">MathWorld: Riemann Zeta Function</a>
%F Equals Sum_{k>=1} (cosh(1/k) - 1). - _Vaclav Kotesovec_, Mar 04 2016
%e 0.86900199196290899881105480556139568889249484188057785071064577856...
%p evalf(Sum(cosh(1/n)-1, n=1..infinity), 120); # _Vaclav Kotesovec_, Mar 04 2016
%t digits = 105; z[k_] := z[k] = z[k-1] + N[Sum[Zeta[2n]/(2n)!, {n, 2^(k-1) + 1, 2^k}], digits]; z[0] = N[Pi^2/12, digits]; rd[k_] := rd[k] = RealDigits[z[k]][[1]]; rd[0]; rd[k = 1]; While[rd[k] != rd[k-1], k++]; rd[k] (* _Jean-François Alcover_, Nov 09 2012 *)
%o (PARI) suminf(n=1, zeta(2*n)/(2*n)!) \\ _Michel Marcus_, Mar 20 2017
%Y Cf. A076813, A093720, A269574, A269611.
%K nonn,cons
%O 0,1
%A _Eric W. Weisstein_, Apr 12 2004
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