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A336810
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Continued fraction expansion of Sum_{k>=0} 1/(k!)!.
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2
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2, 1, 1, 179, 2, 1196852626800230399, 1, 1, 179, 1, 1
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OFFSET
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0,1
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COMMENTS
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a(11), a(21), and a(41) have 152, 1349, and 12981 digits, respectively.
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LINKS
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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).
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FORMULA
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The peak terms have the form ((k+1)!)! / ((k!)!)^2 - 1. - Georg Fischer, Oct 19 2022 [pers. comm. with J. Shallit]
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MATHEMATICA
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ContinuedFraction[Sum[1/(k!)!, {k, 0, 6}], 21] (* Amiram Eldar, Nov 22 2020 *)
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PROG
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(PARI) contfrac(suminf(k=0, 1/(k!)!))
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CROSSREFS
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Cf. A336686 (decimal expansion).
Sequence in context: A159767 A169658 A330199 * A178473 A164810 A322392
Adjacent sequences: A336807 A336808 A336809 * A336811 A336812 A336813
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KEYWORD
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nonn,cofr
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AUTHOR
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Daniel Hoyt, Nov 20 2020
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STATUS
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approved
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