A078690 - OEIS

%I #18 Mar 26 2024 10:29:35

%S 1,2,30,12,1,1,17,90,27,1,1,32,150,42,1,1,47,210,57,1,1,62,270,72,1,1,

%T 77,330,87,1,1,92,390,102,1,1,107,450,117,1,1,122,510,132,1,1,137,570,

%U 147,1,1,152,630,162,1,1,167,690,177,1,1,182,750,192,1,1,197,810,207

%N Continued fraction expansion of e^(2/5).

%H G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>

%H K. Matthews, <a href="http://www.numbertheory.org/php/davison.html">Finding the continued fraction of e^(l/m)</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,2,0,0,0,0,-1).

%F For k>=0, a(5k+1)=15k+2 a(5k+2)=60k+30 a(5k+3)=15k+12 a(5k)=a(5k+4)=1.

%F G.f.: -(x^9-3*x^8-30*x^7-13*x^6+x^5-x^4-12*x^3-30*x^2-2*x-1) / ((x-1)^2*(x^4+x^3+x^2+x+1)^2). - _Colin Barker_, Jun 24 2013

%t Block[{$MaxExtraPrecision=1000},ContinuedFraction[E^(2/5),70]] (* _Harvey P. Dale_, Sep 04 2011 *)

%o (PARI) contfrac(exp(2/5))

%Y Cf. A069951.

%K cofr,nonn,easy

%O 0,2

%A _Benoit Cloitre_, Dec 17 2002