

A336810


Continued fraction expansion of Sum_{k>=0} 1/(k!)!.


2



2, 1, 1, 179, 2, 1196852626800230399, 1, 1, 179, 1, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)



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. 237250 (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]


MATHEMATICA

ContinuedFraction[Sum[1/(k!)!, {k, 0, 6}], 21] (* Amiram Eldar, Nov 22 2020 *)


PROG

(PARI) contfrac(suminf(k=0, 1/(k!)!))


CROSSREFS

Cf. A336686 (decimal expansion).
Sequence in context: A159767 A169658 A330199 * A178473 A164810 A322392
Adjacent sequences: A336807 A336808 A336809 * A336811 A336812 A336813


KEYWORD

nonn,cofr


AUTHOR

Daniel Hoyt, Nov 20 2020


STATUS

approved



