A050924 a(n) = (a(n-1)+1)^(a(n-1)), a(0) = 0.

0, 1, 2, 9, 1000000000

Offset

0,3

Comments

Let S(1) c S(2) c ... c S(n) c ... be an increasing sequence of sets of partial functions that is defined as follows: S(0) = empty set, S(n) = {partial functions: S(n-1) -> S(n-1)}. Then |S(n)| = a(n). - Jon Awbrey, Jul 04 2005

Links

Table of n, a(n) for n=0..4.

J. Awbrey, Riffs and Rotes

Mathematica

NestList[(#+1)^#&, 0, 4] (* Harvey P. Dale, Aug 13 2020 *)

Crossrefs

Cf. A109300, A109301.

Sequence in context: A309861 A140319 A120314 * A181500 A189876 A189867

Adjacent sequences: A050921 A050922 A050923 * A050925 A050926 A050927

Keyword

easy,nonn

Author

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 30 1999

Extensions

The next term is approximately e * 10^9000000000, with nine-place accuracy. - Franklin T. Adams-Watters, Nov 16 2006

a(5) = 2.7182818270999043223766*10^9000000000 = e * 10^9000000000 * 0.9999999995000000004583. - Jon E. Schoenfield, Nov 24 2013

Status

approved