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 A268646 #23 Apr 15 2021 13:12:59
%S A268646 1,1,3,19,277,11081,1383243,569441699,791393701997,3770885471695081,
%T A268646 62402464265309818563,3626978195203590614565619,
%U A268646 747715555141652980441024051237,551447343768097359581617325419468841,1465935896222119146302554598601016693710363
%N A268646 O.g.f.: 1/(1 - C(1)x/(1 - C(2)x/(1 - C(3)x/(1 - C(4)x/(1 - C(5)x/(1 - C(6)x/(1 -...))))))), a continued fraction, where C(n) are the Catalan numbers A000108.
%H A268646 Seiichi Manyama, <a href="/A268646/b268646.txt">Table of n, a(n) for n = 0..61</a>
%F A268646 G.f.: 1/(1 - x/(1 - 2x/(1 - 5x/(1 - 14x/(1 - 42x/(1 -...)))))), by definition.
%F A268646 a(n) ~ c * A003046(n) ~ c * A^(3/2) * 2^(n^2+n-19/24) * exp(3*n/2-1/8) / (n^(3*n/2+15/8) * Pi^(n/2+1)), where A is the Glaisher-Kinkelin constant A074962 and c = 1/Product_{k>=1} (1 - 1/4^k) = 1/QPochhammer[1/4] = 1.452353642449597... - _Vaclav Kotesovec_, Aug 26 2017
%t A268646 Table[SeriesCoefficient[Series[1/(1+ContinuedFractionK[-CatalanNumber[k]*x,1, {k,1,50}]),{x,0,50}],n],{n,1,50}]
%Y A268646 Cf. A000108, A003046.
%K A268646 nonn,easy
%O A268646 0,3
%A A268646 _Benedict W. J. Irwin_, Feb 09 2016
%E A268646 a(0) = 1 added by _Peter Bala_, Apr 17 2017