This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A129409 #9 Feb 13 2015 02:24:34
%S A129409 2,2,2,14,94,372,1391,7690,17729,49204,87816,128433,151275,290477,
%T A129409 297212,299837,352249,897751,1081032,1646358,2402614,36591866,
%U A129409 49132456,93538655,141789387,180474393,687775235,851204316,1868593596,7042652755
%N A129409 Engel expansion of L(3, chi3), where L(s, chi3) is the Dirichlet L-function for the non-principal character modulo 3.
%C A129409 Contributed to OEIS on Apr 15 2007 --- the 300th anniversary of the birth of Leonhard Euler.
%D A129409 Leonhard Euler, "Introductio in Analysin Infinitorum", First Part, Articles 176 and 292
%F A129409 chi3(k) = Kronecker(-3, k); chi3(k) is 0, 1, -1 when k reduced modulo 3 is 0, 1, 2, respectively; chi3 is A049347 shifted.
%F A129409 Series: L(3, chi3) = sum_{k >=1} chi3(k) k^{-3} = 1 - 1/2^3 + 1/4^3 - 1/5^3 + 1/7^3 - 1/8^3 + 1/10^3 - 1/11^3 + ...
%F A129409 Closed form: L(3, chi3) = 4 Pi^3/(81 sqrt(3)).
%e A129409 L(3, chi3) = 0.8840238117500798567430579168710118077... = 1/2 + 1/(2*2) + 1/(2*2*2) + 1/(2*2*2*14) + 1/(2*2*2*14*94) + ...
%t A129409 nmax = 100; prec = 2000 (* Adjust the precision depending on nmax. *); c = N[ 4 Pi^3/(81 Sqrt[3]), prec]; First@Transpose@NestList[{Ceiling[1/(#[[1]] #[[2]] - 1)], #[[1]] #[[2]] - 1}&, {Ceiling[1/c], c}, nmax - 1]
%Y A129409 Cf. A129404, A129405, A129406, A129407, A129408, A129410, A129411.
%Y A129409 Cf. A129658, A129659, A129660, A129661, A129662, A129663, A129664, A129665.
%K A129409 nonn,easy
%O A129409 1,1
%A A129409 _Stuart Clary_, Apr 15 2007