A093720 Decimal expansion of Sum_{n >= 2} zeta(n)/n!.

1, 0, 7, 8, 1, 8, 8, 7, 2, 9, 5, 7, 5, 8, 1, 8, 4, 8, 2, 7, 5, 8, 2, 6, 5, 4, 3, 6, 7, 6, 9, 8, 3, 2, 3, 8, 1, 7, 0, 7, 2, 1, 9, 6, 0, 9, 6, 7, 2, 3, 4, 7, 1, 6, 0, 0, 3, 7, 1, 7, 0, 2, 0, 7, 8, 0, 0, 7, 1, 5, 2, 3, 0, 0, 3, 2, 7, 8, 4, 3, 4, 8, 6, 5, 6, 7, 6, 7, 6, 8, 0, 8, 8, 5, 8, 2, 9, 0, 1

Offset: 1

Author

Eric W. Weisstein, Apr 12 2004

Keywords

• nonn
• cons

Examples

			1.078188729575818482758265436769832381707219...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• J. Sondow and E. W. Weisstein, MathWorld: Riemann Zeta Function

Crossrefs

Cf. A076813, A093721, A269574, A269611, A269720, A269768.

Programs

Maple

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

Mathematica

digits = 99; ClearAll[z, rd]; z[k_] := z[k] = z[k-1] + N[Sum[Zeta[n]/n!, {n, 2^(k-1) + 1, 2^k}], digits]; z[0] = 0; 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 *)

PARI

suminf(n=2, zeta(n)/n!) \\ Michel Marcus, Mar 15 2017

Formula

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

Equals Integral_{x=0..oo} exp(1/(x^2 + 1))*sin(x/(x^2 + 1))*(coth(Pi*x) - 1) dx + A091725 - 2*A001620 - exp(1)/2 + 3/2. - Velin Yanev, Nov 14 2024

Extensions

Corrected by Fredrik Johansson, Mar 19 2006