a(n) = (-1)^n * Sum_{2*m + 1 | 2*n + 1} (-1)^m (2*m + 1)^4.

Terms

a(0) =1a(1) =80a(2) =626a(3) =2400a(4) =6481a(5) =14640a(6) =28562a(7) =50080a(8) =83522a(9) =130320a(10) =192000a(11) =279840a(12) =391251a(13) =524960a(14) =707282a(15) =923520a(16) =1171200a(17) =1502400a(18) =1874162a(19) =2284960a(20) =2825762a(21) =3418800a(22) =4057106a(23) =4879680a(24) =5762401a(25) =6681760a(26) =7890482a(27) =9164640a(28) =10425600