a(n) has generating function 1/((1-x)^k*(1-x^2)^(k*(k-1)/2)) for k=5.

Terms

a(0) =1a(1) =5a(2) =25a(3) =85a(4) =275a(5) =751a(6) =1955a(7) =4615a(8) =10460a(9) =22220a(10) =45628a(11) =89420a(12) =170340a(13) =313140a(14) =562020a(15) =980628a(16) =1676370a(17) =2800410a(18) =4596290a(19) =7399930a(20) =11732006a(21) =18297950a(22) =28155910a(23) =42716750a(24) =64037980a(25) =94823756a(26) =138922300a(27) =201325900a(28) =288988100