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

0,1

Links

Robert G. Wilson v, Table of n, a(n) for n = 0..1000 (a(0)-a(105) from Vaclav Kotesovec)

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).

Example

0.9361913194044870516411920348031344882476706274072832788436119459958471789...

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]]

Crossrefs

Cf. A098572, A363704.

Sequence in context: A230158 A307960 A224235 * A169849 A182547 A019737

Adjacent sequences: A363713 A363714 A363715 * A363717 A363718 A363719

Keyword

nonn,cons

Author

Vaclav Kotesovec, Jun 17 2023

Status

approved