

A336810


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


4



2, 1, 1, 179, 2, 1196852626800230399, 1, 1, 179, 1, 1
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OFFSET

0,1


COMMENTS

a(11), a(21), and a(41) have 152, 1349, and 12981 digits, respectively.


LINKS

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]
Let P(k) = ((k+1)!)! / ((k!)!)^2  1. After the first term, the rest of the sequence is an interleaving between the nth 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



STATUS

approved



