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 A336810 Continued fraction expansion of Sum_{k>=0} 1/(k!)!. 4
 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 Daniel Hoyt, Python program that generates the continued fraction from formula. 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 Cf. A336686 (decimal expansion). Cf. A001511, A157196, A363841. 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 August 13 20:30 EDT 2024. Contains 375144 sequences. (Running on oeis4.)