%I #12 Apr 03 2021 09:47:05

%S 1,1,1,1,2,1,1,3,4,3,1,4,10,24,10,1,5,20,105,160,105,1,6,35,336,1260,

%T 3360,1260,1,7,56,882,6720,48510,80640,48510,1,8,84,2016,27720,443520,

%U 2162160,6209280,2162160,1,9,120,4158,95040,2972970,34594560,312161850

%N Triangular array for David G. Cantor's sigma function.

%H D. G. Cantor, <a href="http://www.digizeitschriften.de/dms/resolveppn/?PID=GDZPPN002211343">On the analogue of the division polynomials for hyperelliptic curves</a>, J. Reine Angew. Math. (Crelle's J.) 447 (1994), pp. 91-145.

%F T(n, k)*T(n-2, k-1)-2*T(n-1, k-1)*T(n-1, k)+T(n, k-1)*T(n-2, k)=0.

%e Triangle rows:

%e 1;

%e 1,1;

%e 1,2,1;

%e 1,3,4,3;

%e 1,4,10,24,10;

%e 1,5,20,105,160,105;

%e ...

%o (PARI) {T(n, k) = if( k<0 || k>n, 0, prod( i=1, (k+1)\2, binomial(n + 2*i - 1 - k%2, 4*i - 1 - k%2*2)))}

%K nonn,tabl,easy

%O 0,5

%A _Michael Somos_, Jun 12 2000