a(n) = Sum_{i=1..floor(n/2)} (n-i)^i.

Terms

a(0) =0a(1) =1a(2) =2a(3) =7a(4) =13a(5) =48a(6) =95a(7) =424a(8) =898a(9) =4837a(10) =10780a(11) =68399a(12) =158111a(13) =1156224a(14) =2745145a(15) =22744380a(16) =55098660a(17) =510307001a(18) =1255610350a(19) =12859037607a(20) =32030878113a(21) =359498491968a(22) =904385401323