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A093721 Decimal expansion of Sum_{n>=1} zeta(2n)/(2n)!.

%I A093721 #22 Feb 16 2025 08:32:53
%S A093721 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 A093721 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 A093721 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 A093721 Decimal expansion of Sum_{n>=1} zeta(2n)/(2n)!.
%H A093721 G. C. Greubel, <a href="/A093721/b093721.txt">Table of n, a(n) for n = 0..10000</a>
%H A093721 J. Sondow and E. W. Weisstein, <a href="https://mathworld.wolfram.com/RiemannZetaFunction.html">MathWorld: Riemann Zeta Function</a>
%F A093721 Equals Sum_{k>=1} (cosh(1/k) - 1). - _Vaclav Kotesovec_, Mar 04 2016
%e A093721 0.86900199196290899881105480556139568889249484188057785071064577856...
%p A093721 evalf(Sum(cosh(1/n)-1, n=1..infinity), 120); # _Vaclav Kotesovec_, Mar 04 2016
%t A093721 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 A093721 (PARI) suminf(n=1, zeta(2*n)/(2*n)!) \\ _Michel Marcus_, Mar 20 2017
%Y A093721 Cf. A076813, A093720, A269574, A269611.
%K A093721 nonn,cons
%O A093721 0,1
%A A093721 _Eric W. Weisstein_, Apr 12 2004