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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. 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]

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

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Last modified February 3 03:08 EST 2023. Contains 360024 sequences. (Running on oeis4.)