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%I #11 Dec 09 2020 11:20:24
%S 1,1,1,1,2,2,4,4,2,10,10,4,24,24,14,4,66,66,34,8,174,174,106,42,8,504,
%T 504,284,98,16,1406,1406,878,390,114,16,4210,4210,2486,1002,258,32,
%U 12198,12198,7738,3652,1270,290,32,37378,37378,22714,9962,3140,642,64,111278,111278,71370,34986,13370,3794,706,64
%N Irregular triangle read by rows: for n >= 2, 2 <= k <= floor(n/2) + 1, T(n,k) = the number of semi-meanders with n top arches, a first arch of length one and k arch groupings.
%F T(2,2) = T(3,2) = 1.
%F For n >= 4, T(n,2) = T(n,3) = A000682(n-2).
%F For n >= 6 and k >= 4, T(n,k) = Sum {x = k-1..floor(n/2)} (A259689(T(n-2,x))).
%F For n >= 4, A301620(n-3) = Sum {k = 4..floor((n+2)/2)} (T(n,k)).
%e For n = 6: /\ = arch of length one;
%e /\ /\ /\ /\
%e / \ //\\ / \ //\\ 4 with 2 groupings
%e / /\\ // \\ / \ ///\\\
%e / / \\ // /\\\ //\ /\\ ////\\\\
%e /\ //\//\/\\\, /\ ///\//\\\\, /\ ///\\//\\\, /\ /////\\\\\,
%e /\ /\
%e //\\ /\ /\ / \ 4 with 3 groupings
%e ///\\\ /\ //\\ //\\ /\ //\ \
%e /\ /\ ////\\\\, /\ //\\ ///\\\, /\ ///\\\ //\\, /\ /\ ///\\/\\,
%e /\ 2 with 4 groupings
%e / \ /\ /\
%e /\ /\ /\ //\/\\, /\ //\\ /\ //\\, T(6,2) = 4, T(6,3) = 4, T(6,4) = 2;
%e Irregular triangle begins:
%e n\k (2) (3) (4) (5) (6)
%e 2: 1
%e 3: 1
%e 4: 1 1
%e 5: 2 2
%e 6: 4 4 2
%e 7: 10 10 4
%e 8: 24 24 14 4
%e 9: 66 66 34 8
%e 10: 174 174 106 42 8
%e ...
%Y Cf. A259689, A301620, Row sums: A000682(n-1).
%K nonn,tabf
%O 2,5
%A _Roger Ford_, Nov 26 2020
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