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%I #14 Feb 15 2020 10:44:42
%S 1,1,2,4,8,18,42,108,282,786,2192,6402,18600,55978,167256,514102,
%T 1567976,4896164,15170630,47957260,150468678,480371736,1522649458,
%U 4900568718,15665593150,50761432998,163431901126,532624603680,1725349278270,5650796083020,18401781369182
%N The number of semi-meanders with n top arches and concentric arches within the starting arch or a starting arch with length one.
%H Jean-François Alcover, <a href="/A330269/b330269.txt">Table of n, a(n) for n = 1..46</a>
%F a(1) = 1, for n >= 2, a(n) = Sum_{k=1..n-1} A000682(k).
%e For n = 5, a(5) = 8:
%e /\ /\
%e //\\ /\ / \ /\
%e ///\\\ /\ /\ / \ / /\\ /\ //\\
%e /\////\\\\, /\//\\//\\, /\/\//\/\\, /\//\//\\\, //\\///\\\,
%e /\
%e /\ //\\ starting arch
%e /\ /\ //\\ /\ ///\\\ (1) (2) (3) (4)
%e //\\//\\/\, ///\\\//\\, ////\\\\/\, 4 + 2 + 1 + 1 = 8.
%t A000136 = Import["https://oeis.org/A000136/b000136.txt", "Table"][[All, 2]];
%t a[n_] := If[n == 1, 1, Sum[A000136[[k]]/k, {k, 1, n - 1}]];
%t a /@ Range[46] (* _Jean-François Alcover_, Feb 13 2020 *)
%Y Cf. A000682.
%K nonn
%O 1,3
%A _Roger Ford_, Dec 07 2019
%E More terms from _Jinyuan Wang_, Dec 08 2019
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