OFFSET
0,1
COMMENTS
a(11), a(21), and a(41) have 152, 1349, and 12981 digits, respectively.
LINKS
Georg Fischer, Table of n, a(n) for n = 0..20
Georg Fischer, Table of n, a(n) for n = 0..139
Alfred J. van der Poorten and Jeffrey Shallit, Folded continued fractions, Journal of Number Theory, Vol. 40, Issue 2, 1992, pp. 237-250 (cf. prop. 2).
FORMULA
The peak terms have the form ((k+1)!)! / ((k!)!)^2 - 1. - Georg Fischer, Oct 19 2022 [pers. comm. with J. Shallit]
Let P(k) = ((k+1)!)! / ((k!)!)^2 - 1. After the first term, the rest of the sequence is an interleaving between the n-th runs of '1, 1' and '2' in A157196, and P(A001511(n)+1). - Daniel Hoyt, Jun 26 2023
MATHEMATICA
ContinuedFraction[Sum[1/(k!)!, {k, 0, 6}], 21] (* Amiram Eldar, Nov 22 2020 *)
PROG
(PARI) contfrac(suminf(k=0, 1/(k!)!))
CROSSREFS
KEYWORD
nonn,cofr
AUTHOR
Daniel Hoyt, Nov 20 2020
STATUS
approved