login
Triangle read by rows: T(n,k) is the number of polygons with 2*n sides, of which k run through the center of a circle, on the circumference of which the 2*n vertices of the polygon are arranged at equal spacing, up to rotation.
1

%I #22 Dec 05 2022 04:40:53

%S 0,0,1,1,0,1,4,4,4,2,98,120,84,24,6,5648,6912,4032,1344,288,40,532344,

%T 631680,351360,118408,26400,3840,322,72724122,84211200,45907200,

%U 15436800,3513600,552960,57600,3294,13577195574,15432560640,8305920000,2786273280,643507200,106122240,12418560,967680,40320

%N Triangle read by rows: T(n,k) is the number of polygons with 2*n sides, of which k run through the center of a circle, on the circumference of which the 2*n vertices of the polygon are arranged at equal spacing, up to rotation.

%C By "2*n-sided polygons" we mean the polygons that can be drawn by connecting 2*n equally spaced points on a circle.

%C T(0,0)=0 and T(0,1)=1 by convention.

%C The sequence is limited to even-sided polygons, since all odd-sided polygons have no side passing through the center.

%H Ludovic Schwob, <a href="/A358328/b358328.txt">Table of n, a(n) for n = 0..5150</a>

%e Triangle begins:

%e 0;

%e 0, 1;

%e 1, 0, 1;

%e 4, 4, 4, 2;

%e 98, 120, 84, 24, 6;

%Y Row sums give A094155(n).

%Y Cf. A330662.

%K nonn,tabl

%O 0,7

%A _Ludovic Schwob_, Nov 09 2022