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A293961 Number T(n,k) of linear chord diagrams having n chords and maximal chord length k (or k=0 if n=0); triangle T(n,k), n>=0, 0<=k<=n, read by rows.

%I A293961 #17 Nov 05 2020 19:40:59
%S A293961 1,0,1,0,1,2,0,1,4,10,0,1,10,24,70,0,1,20,82,212,630,0,1,42,300,798,
%T A293961 2324,6930,0,1,84,894,3800,10078,30188,90090,0,1,170,2744,18186,51804,
%U A293961 150046,452724,1351350,0,1,340,8594,71624,313006,851692,2545390,7695828,22972950
%N A293961 Number T(n,k) of linear chord diagrams having n chords and maximal chord length k (or k=0 if n=0); triangle T(n,k), n>=0, 0<=k<=n, read by rows.
%C A293961 All terms in columns k > 1 are even.
%H A293961 Alois P. Heinz, <a href="/A293961/b293961.txt">Rows n = 0..20, flattened</a>
%F A293961 A(n,k) = A293960(n,k) - A293960(n,k-1) for k>0, A(n,0) = A000007(n).
%e A293961 Triangle T(n,k) begins:
%e A293961   1;
%e A293961   0, 1;
%e A293961   0, 1,   2;
%e A293961   0, 1,   4,   10;
%e A293961   0, 1,  10,   24,    70;
%e A293961   0, 1,  20,   82,   212,   630;
%e A293961   0, 1,  42,  300,   798,  2324,   6930;
%e A293961   0, 1,  84,  894,  3800, 10078,  30188,  90090;
%e A293961   0, 1, 170, 2744, 18186, 51804, 150046, 452724, 1351350;
%e A293961   ...
%Y A293961 Columns k=0-2 give: A000007, A057427, A167030(n+1).
%Y A293961 Row sums give A001147.
%Y A293961 Main diagonal gives A293962.
%Y A293961 T(2n,n) gives A293963.
%Y A293961 Cf. A293881, A293960.
%K A293961 nonn,tabl
%O A293961 0,6
%A A293961 _Alois P. Heinz_, Oct 20 2017