A247551 Decimal expansion of Product_{k>=2} 1/(1-1/k!).

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

Offset

1,1

Links

Table of n, a(n) for n=1..105.

Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 269.

A. Knopfmacher, A. M. Odlyzko, B. Pittel, L. B. Richmond, D. Stark, G. Szekeres, and N. C. Wormald, The Asymptotic Number of Set Partitions with Unequal Block Sizes, The Electronic Journal of Combinatorics, Volume 6 (1999), Research Paper #R2.

Formula

Product_{k>=2} 1/(1-1/k!).

Equals lim_{n -> oo} A005651(n) / n!.

Equals 1/A282529. - Amiram Eldar, Sep 15 2023

Example

2.5294774720791526481801161542539542411787023948459973375849349825...

Maple

evalf(1/product(1-1/k!, k=2..infinity), 100); # Vaclav Kotesovec, Sep 19 2014

Mathematica

digits = 105;
RealDigits[NProduct[1/(1-1/k!), {k, 2, Infinity}, WorkingPrecision -> digits+10, NProductFactors -> digits], 10, digits][[1]] (* Jean-François Alcover, Nov 02 2020 *)

Prog

(PARI) default(realprecision, 150); 1/prodinf(k=2, 1 - 1/k!) \\ Vaclav Kotesovec, Sep 21 2014

Crossrefs

Cf. A005651, A035341, A072605, A140585, A183239, A209668, A261600, A282529, A292713, A320566, A327827, A335643.

Sequence in context: A131201 A070633 A266256 * A347378 A336853 A273580

Adjacent sequences: A247548 A247549 A247550 * A247552 A247553 A247554

Keyword

nonn,cons,easy

Author

Vaclav Kotesovec, Sep 19 2014

Status

approved