A336730 Decimal expansion of Sum_{n>=1} log(n)^n / n!.

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

Offset

0,1

Comments

With u(n) = log(n)^n / n!, this series is convergent as u(n+1)/u(n) -> 0 when n -> oo.

References

Jean-Marie Monier, Analyse, Exercices corrigés, 2ème année, MP, Dunod, 1997, Exercice 3.2.1.r page 279.

Links

Table of n, a(n) for n=0..104.

Formula

Equals Sum_{n>=1} log(n)^n / n!.

Example

0.785672099547734935860778589192856069327...

Maple

evalf(sum(log(n)^n/n!, n=2..infinity), 120);

Prog

(PARI) suminf(n=1, log(n)^n/n!) \\ Michel Marcus, Aug 02 2020

Crossrefs

Cf. A099871, A306243, A308915, A336284.

Sequence in context: A031139 A215733 A226750 * A021564 A021060 A117239

Adjacent sequences: A336727 A336728 A336729 * A336731 A336732 A336733

Keyword

nonn,cons

Author

Bernard Schott, Aug 02 2020

Status

approved