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

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, 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, 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

Offset

0,1

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

J. Sondow and E. W. Weisstein, MathWorld: Riemann Zeta Function

Formula

Equals Sum_{k>=1} (cosh(1/k) - 1). - Vaclav Kotesovec, Mar 04 2016

Example

0.86900199196290899881105480556139568889249484188057785071064577856...

Maple

evalf(Sum(cosh(1/n)-1, n=1..infinity), 120); # Vaclav Kotesovec, Mar 04 2016

Mathematica

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 *)

Prog

(PARI) suminf(n=1, zeta(2*n)/(2*n)!) \\ Michel Marcus, Mar 20 2017

Crossrefs

Cf. A076813, A093720, A269574, A269611.

Sequence in context: A362439 A110214 A305709 * A091506 A021539 A084893

Adjacent sequences: A093718 A093719 A093720 * A093722 A093723 A093724

Keyword

nonn,cons

Author

Eric W. Weisstein, Apr 12 2004

Status

approved