cp's OEIS Frontend

A363716 Decimal expansion of Sum_{k>=2} (1/k!) * k-th derivative of zeta(k).

%I A363716 #14 Jun 18 2023 11:41:29
%S A363716 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,
%T A363716 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,
%U A363716 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
%N A363716 Decimal expansion of Sum_{k>=2} (1/k!) * k-th derivative of zeta(k).
%H A363716 Robert G. Wilson v, <a href="/A363716/b363716.txt">Table of n, a(n) for n = 0..1000</a> (a(0)-a(105) from _Vaclav Kotesovec_)
%F A363716 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).
%e A363716 0.9361913194044870516411920348031344882476706274072832788436119459958471789...
%t A363716 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]]
%Y A363716 Cf. A098572, A363704.
%K A363716 nonn,cons
%O A363716 0,1
%A A363716 _Vaclav Kotesovec_, Jun 17 2023