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 A068380 Engel expansion of sinh(1/3). 1
 3, 54, 180, 378, 648, 990, 1404, 1890, 2448, 3078, 3780, 4554, 5400, 6318, 7308, 8370, 9504, 10710, 11988, 13338, 14760, 16254, 17820, 19458, 21168, 22950, 24804, 26730, 28728, 30798, 32940, 35154, 37440, 39798, 42228, 44730, 47304, 49950 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Cf. A006784 for the definition of the Engel expansion. The MathWorld link mentions the closed form of the Engel expansion of sinh(1). - Georg Fischer, Nov 22 2020 LINKS Eric W. Weisstein, Engel Expansion Wikipedia, Engel Expansion Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(1) = 3, a(n) = 18*(n*(2*n-3)+1 for n>1. - Ralf Stephan, Sep 03 2003 a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>4. G.f.: 3*x*(x^3-9*x^2-15*x-1)/(x-1)^3. - Colin Barker, Apr 13 2012 EXAMPLE 1/3 + 1/(3*54) + 1/(3*54*180) + 1/(3*54*180*378) + 1/(3*54*180*378*648) ...           = 0.3395405572560086... sinh(1/3) = 0.33954055725615013910126061... MATHEMATICA LinearRecurrence[{3, -3, 1}, {3, 54, 180, 378}, 50] PROG (PARI) a(n)=if(n<=1, 3, 18*(n*(2*n-3)+1)) CROSSREFS Cf. A006784, A068379. Sequence in context: A344424 A045481 A275566 * A174782 A345074 A119294 Adjacent sequences:  A068377 A068378 A068379 * A068381 A068382 A068383 KEYWORD easy,nonn AUTHOR Benoit Cloitre, Mar 03 2002 EXTENSIONS Edited, offset 1 and a(1)=3 by Georg Fischer, Nov 23 2020 STATUS approved

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Last modified September 17 01:53 EDT 2021. Contains 347478 sequences. (Running on oeis4.)