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

Author

Vaclav Kotesovec, Sep 19 2014

Keywords

• nonn
• cons
• easy

Examples

			2.5294774720791526481801161542539542411787023948459973375849349825...
		

Links

• 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.

Crossrefs

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

Programs

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 *)

PARI

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

Formula

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

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

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