T(n,k)=Number of nondecreasing arrangements of n numbers in -(n+k-2)..(n+k-2) with sum zero.

Terms

a(0) =1a(1) =1a(2) =2a(3) =1a(4) =3a(5) =5a(6) =1a(7) =4a(8) =8a(9) =18a(10) =1a(11) =5a(12) =13a(13) =33a(14) =73a(15) =1a(16) =6a(17) =18a(18) =55a(19) =141a(20) =338a(21) =1a(22) =7a(23) =25a(24) =86a(25) =252a(26) =676a(27) =1656a(28) =1a(29) =8