a(n) = n*(1 - (-1)^n - 2*(3 + (-1)^n)*n^2 + 2*n^4)/384.

Terms

a(0) =0a(1) =0a(2) =0a(3) =1a(4) =4a(5) =15a(6) =36a(7) =84a(8) =160a(9) =300a(10) =500a(11) =825a(12) =1260a(13) =1911a(14) =2744a(15) =3920a(16) =5376a(17) =7344a(18) =9720a(19) =12825a(20) =16500a(21) =21175a(22) =26620a(23) =33396a(24) =41184a(25) =50700a(26) =61516a(27) =74529a(28) =89180a(29) =106575