A293961 - OEIS

%I #17 Nov 05 2020 19:40:59

%S 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 2324,6930,0,1,84,894,3800,10078,30188,90090,0,1,170,2744,18186,51804,

%U 150046,452724,1351350,0,1,340,8594,71624,313006,851692,2545390,7695828,22972950

%N 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 All terms in columns k > 1 are even.

%H Alois P. Heinz, <a href="/A293961/b293961.txt">Rows n = 0..20, flattened</a>

%F A(n,k) = A293960(n,k) - A293960(n,k-1) for k>0, A(n,0) = A000007(n).

%e Triangle T(n,k) begins:

%e   1;

%e   0, 1;

%e   0, 1,   2;

%e   0, 1,   4,   10;

%e   0, 1,  10,   24,    70;

%e   0, 1,  20,   82,   212,   630;

%e   0, 1,  42,  300,   798,  2324,   6930;

%e   0, 1,  84,  894,  3800, 10078,  30188,  90090;

%e   0, 1, 170, 2744, 18186, 51804, 150046, 452724, 1351350;

%e   ...

%Y Columns k=0-2 give: A000007, A057427, A167030(n+1).

%Y Row sums give A001147.

%Y Main diagonal gives A293962.

%Y T(2n,n) gives A293963.

%Y Cf. A293881, A293960.

%K nonn,tabl

%O 0,6

%A _Alois P. Heinz_, Oct 20 2017