A363716 Decimal expansion of Sum_{k>=2} (1/k!) * k-th derivative of zeta(k).
9, 3, 6, 1, 9, 1, 3, 1, 9, 4, 0, 4, 4, 8, 7, 0, 5, 1, 6, 4, 1, 1, 9, 2, 0, 3, 4, 8, 0, 3, 1, 3, 4, 4, 8, 8, 2, 4, 7, 6, 7, 0, 6, 2, 7, 4, 0, 7, 2, 8, 3, 2, 7, 8, 8, 4, 3, 6, 1, 1, 9, 4, 5, 9, 9, 5, 8, 4, 7, 1, 7, 8, 9, 1, 6, 3, 7, 0, 0, 5, 6, 4, 9, 3, 3, 6, 3, 3, 8, 3, 9, 6, 2, 3, 6, 1, 1, 4, 5, 7, 2, 4, 8, 0, 2, 4
Offset: 0
Examples
0.9361913194044870516411920348031344882476706274072832788436119459958471789...
Links
- Robert G. Wilson v, Table of n, a(n) for n = 0..1000 (a(0)-a(105) from _Vaclav Kotesovec_)
Programs
-
Mathematica
digits = 120; d = 1; j = 2; s = 0; While[Abs[d] > 10^(-digits - 5), d = 1 / j! * Derivative[j][Zeta][j]; s += d; j++]; RealDigits[s, 10, 120][[1]]
Formula
Equals lim_{n->oo} (Sum_{m=1..n} 1/m^(1/m)) - n + log(n)^2/2 + sg1, where sg1 is the first Stieltjes constant (see A082633).