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A293881 Number T(n,k) of linear chord diagrams having n chords and minimal chord length k (or k=0 if n=0); triangle T(n,k), n>=0, 0<=k<=n, read by rows.

%I A293881 #20 Nov 05 2020 19:40:24
%S A293881 1,0,1,0,2,1,0,10,4,1,0,69,26,9,1,0,616,230,79,19,1,0,6740,2509,854,
%T A293881 252,39,1,0,87291,32422,11105,3441,796,79,1,0,1305710,484180,167273,
%U A293881 52938,14296,2468,159,1,0,22149226,8203519,2855096,919077,265103,59520,7564,319,1
%N A293881 Number T(n,k) of linear chord diagrams having n chords and minimal chord length k (or k=0 if n=0); triangle T(n,k), n>=0, 0<=k<=n, read by rows.
%C A293881 Conjecture: column k>0 is asymptotic to (exp(-k+1) - exp(-k)) * 2^(n + 1/2) * n^n / exp(n). - _Vaclav Kotesovec_, Oct 25 2017
%e A293881 Triangle T(n,k) begins:
%e A293881   1;
%e A293881   0,       1;
%e A293881   0,       2,      1;
%e A293881   0,      10,      4,      1;
%e A293881   0,      69,     26,      9,     1;
%e A293881   0,     616,    230,     79,    19,     1;
%e A293881   0,    6740,   2509,    854,   252,    39,    1;
%e A293881   0,   87291,  32422,  11105,  3441,   796,   79,   1;
%e A293881   0, 1305710, 484180, 167273, 52938, 14296, 2468, 159,  1;
%e A293881   ...
%Y A293881 Columns k=0-10 give: A000007, A293914, A293915, A293916, A293917, A293918, A293919, A293920, A293921, A293922, A293923.
%Y A293881 Row sums give A001147.
%Y A293881 T(2n,n) gives A290688.
%Y A293881 Main diagonal and first lower diagonal give: A000012, A054135 (for n>0).
%Y A293881 Cf. A293157, A293961.
%K A293881 nonn,tabl
%O A293881 0,5
%A A293881 _Alois P. Heinz_, Oct 18 2017