Number of integer compositions of 2n whose half-alternating sum is 0.

Terms

a(0) =1a(1) =0a(2) =2a(3) =8a(4) =28a(5) =104a(6) =396a(7) =1504a(8) =5720a(9) =21872a(10) =83980a(11) =323344a(12) =1248072a(13) =4828784a(14) =18721080a(15) =72711552a(16) =282861360a(17) =1101980000a(18) =4298748300a(19) =16789002736a(20) =65641204200a(21) =256895795312