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 A168441 #21 Feb 07 2025 00:50:40
%S A168441 1,1,3,17,155,2025,34819,743329,18937707,560071193,18844479635,
%T A168441 710440531665,29654234779771,1357326276747721,67589738142784803,
%U A168441 3637403230889380097,210358430818676801675,13009719599952748481145
%N A168441 Expansion of 1/(1-x/(1-2x/(1-4x/(1-6x/(1-8x/(1-.... (continued fraction).
%C A168441 Hankel transform is A168442.
%F A168441 G.f.: 1/(1-x-2x^2/(1-6x-24x^2/(1-14x-80x^2/(1-22x-168x^2/(1-30x-288x^2/(1-... (continued fraction).
%F A168441 a(n) = Sum_{k=0..n} A111106(n,k)*2^(n-k). - _Philippe Deléham_, Nov 28 2009
%F A168441 a(n) = upper left term of M^n, M = an infinite square production matrix as follows:
%F A168441 1, 1, 0, 0, 0, 0, ...
%F A168441 2, 2, 2, 0, 0, 0, ...
%F A168441 4, 4, 4, 4, 0, 0, ...
%F A168441 6, 6, 6, 6, 6, 0, ...
%F A168441 8, 8, 8, 8, 8, 8, ...
%F A168441 ...
%F A168441 (where the series (1,2,4,6,8,...) = A004277, positive even integers prefaced with a 1). - _Gary W. Adamson_, Jul 19 2011
%F A168441 G.f. 1 + x/(G(0)-x) where G(k) = 1 - x*(2*k+2)/G(k+1); (continued fraction). - _Sergei N. Gladkovskii_, Oct 28 2012
%F A168441 a(n) ~ 2^(2*n - 3/2) * n^(n-1) / exp(n). - _Vaclav Kotesovec_, Jan 23 2024
%t A168441 nmax = 20; CoefficientList[1 + x*Series[1/(1 - x + ContinuedFractionK[-2*k*x, 1, {k, 1, nmax}]), {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jan 23 2024 *)
%Y A168441 Cf. A004277, A111106, A168442.
%K A168441 easy,nonn
%O A168441 0,3
%A A168441 _Paul Barry_, Nov 25 2009