A358191 Decimal expansion of Sum_{n >= 2} (n-1)/(n^n).

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

Offset: 0

Author

Peter Bala, Nov 02 2022

Keywords

• cons
• nonn

Examples

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Links

• Eric Weisstein's World of Mathematics, Sophomore's Dream.

Crossrefs

Cf. A073009, A098686.

Programs

Maple

evalf(add((n-1)/n^n, n = 2..65), 100);

PARI

suminf(n=2, (n-1)/n^n) \\ Michel Marcus, Nov 03 2022

Formula

Equals Integral_{x = 0..1} x*log(x)^2/x^x dx.

Equals -Integral_{x = 0..1} x*log(x)/x^x dx.

Equals Integral_{x = 0..1} Integral_{y = 0..1} (x*y)^(1 - x*y) dy dx.

Equals A098686 - A073009.