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 Weisstein's World of Mathematics, 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
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