The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A270138 Continued fraction expansion of the constant 6/A270121(1)+Sum_{n>=2}1/A270121(n). 0
 0, 1, 6, 2, 7, 32, 112, 10800, 403200, 17418254400, 1755760043520000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A270121 is defined by the following recurrence: if A270121(n)=x(n) then x(n+1)*x(n-1)=x(n)^2*(1+n*x(n)) for n>=1, with x(1)=7, x(2)=112; and for A270124, if A270124(n)=y(n) then y(0)=2 and y(n)=x(n+1)/x(n) for n>=1. Both of these sequences appear in this continued fraction expansion, which defines a transcendental number. LINKS A. N. W. Hone, Curious continued fractions, nonlinear recurrences and transcendental numbers, Journal of Integer Sequences, Vol. 18 (2015), Article 15.8.4. A. N. W. Hone, Continued fractions for some transcendental numbers, arXiv:1509.05019 [math.NT], 2015-2016, Monatsh. Math. DOI: 10.1007/s00605-015-0844-2. FORMULA a(2*n+1) = n*A270124(n-1), a(2*n+2) = A270121(n) for n>=1. EXAMPLE 6/A270121(1)+Sum_{n>=2}1/A270121(n)=6/7+1/112+1/403200+1/1755760043520000+... =[0;1,6,2,7,32,112,10800,403200,17418254400,...] =[0;1,6,A270124(0),A270121(1),2*A270124(1),A270121(2),3*A270124(2),A270121(3),4*A270124(3),...] (continued fraction). CROSSREFS Cf. A112373, A114550, A114551, A114552. Sequence in context: A244381 A307086 A021090 * A177889 A086744 A242301 Adjacent sequences: A270135 A270136 A270137 * A270139 A270140 A270141 KEYWORD nonn,cofr AUTHOR Andrew Hone, Mar 11 2016 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 29 00:02 EST 2023. Contains 359905 sequences. (Running on oeis4.)