1 + Sum_{n >= 1} Sum_{k = 0..n-1} (-1)^n*T(n,k)*y^(2*k)*x^(2*n)/(2*n)! = JacobiCN(x,y).

Terms

a(0) =1a(1) =1a(2) =4a(3) =1a(4) =44a(5) =16a(6) =1a(7) =408a(8) =912a(9) =64a(10) =1a(11) =3688a(12) =30768a(13) =15808a(14) =256a(15) =1a(16) =33212a(17) =870640a(18) =1538560a(19) =259328a(20) =1024a(21) =1a(22) =298932a(23) =22945056a(24) =106923008a(25) =65008896a(26) =4180992a(27) =4096a(28) =1a(29) =2690416