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

%I A247551 #41 Jan 20 2024 07:06:38
%S A247551 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,
%T A247551 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,
%U A247551 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
%N A247551 Decimal expansion of Product_{k>=2} 1/(1-1/k!).
%H A247551 Steven R. Finch, <a href="https://doi.org/10.1017/9781316997741">Mathematical Constants II</a>, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 269.
%H A247551 A. Knopfmacher, A. M. Odlyzko, B. Pittel, L. B. Richmond, D. Stark, G. Szekeres, and N. C. Wormald, <a href="https://doi.org/10.37236/1434">The Asymptotic Number of Set Partitions with Unequal Block Sizes</a>, The Electronic Journal of Combinatorics, Volume 6 (1999), Research Paper #R2.
%F A247551 Product_{k>=2} 1/(1-1/k!).
%F A247551 Equals lim_{n -> oo} A005651(n) / n!.
%F A247551 Equals 1/A282529. - _Amiram Eldar_, Sep 15 2023
%e A247551 2.5294774720791526481801161542539542411787023948459973375849349825...
%p A247551 evalf(1/product(1-1/k!,k=2..infinity),100); # _Vaclav Kotesovec_, Sep 19 2014
%t A247551 digits = 105;
%t A247551 RealDigits[NProduct[1/(1-1/k!), {k, 2, Infinity}, WorkingPrecision -> digits+10, NProductFactors -> digits], 10, digits][[1]] (* _Jean-François Alcover_, Nov 02 2020 *)
%o A247551 (PARI) default(realprecision,150); 1/prodinf(k=2,1 - 1/k!) \\ _Vaclav Kotesovec_, Sep 21 2014
%Y A247551 Cf. A005651, A035341, A072605, A140585, A183239, A209668, A261600, A282529, A292713, A320566, A327827, A335643.
%K A247551 nonn,cons,easy
%O A247551 1,1
%A A247551 _Vaclav Kotesovec_, Sep 19 2014