Number of compositions of n into exactly n nonnegative parts with largest part ceiling(n/2).

Terms

a(0) =1a(1) =1a(2) =1a(3) =6a(4) =18a(5) =50a(6) =195a(7) =392a(8) =1652a(9) =2970a(10) =12825a(11) =22022a(12) =96030a(13) =160888a(14) =705341a(15) =1162800a(16) =5116200a(17) =8335338a(18) =36773397a(19) =59366450a(20) =262462010a(21) =420630210a(22) =1862790699a(23) =2967563040a(24) =13160496684a(25) =20861295000a(26) =92624149475a(27) =146203657992a(28) =649794035142