[go: up one dir, main page]

login
Triangular array of ways of drawing k non-intersecting chords between n points on a circle; i.e., Motzkin polynomial coefficients.
4

%I #8 Jul 29 2017 00:20:27

%S 1,1,0,1,1,0,1,3,0,0,1,6,2,0,0,1,10,10,0,0,0,1,15,30,5,0,0,0,1,21,70,

%T 35,0,0,0,0,1,28,140,140,14,0,0,0,0,1,36,252,420,126,0,0,0,0,0,1,45,

%U 420,1050,630,42,0,0,0,0,0,1,55,660,2310,2310,462,0,0,0,0,0,0,1,66,990,4620

%N Triangular array of ways of drawing k non-intersecting chords between n points on a circle; i.e., Motzkin polynomial coefficients.

%F For n >= 2k: T(n, k) = n!/((n-2k)!k!(k+1)!) = A007318(n, 2k)*A000108(k).

%F T(n,k) = A055151(n,k).

%e Rows start: 1; 1,0; 1,1,0; 1,3,0,0; 1,6,2,0,0; 1,10,10,0,0,0; 1,15,30,5,0,0,0; etc.

%Y Visible version of A055151. Row sums are A001006 (Motzkin numbers). Columns include A000012, A000217, A034827 and perhaps A000910.

%K nonn,tabl

%O 0,8

%A _Henry Bottomley_, Jan 31 2003