Constant term of the reduction by x^2 -> x+2 of the polynomial p(n,x) defined below in Comments.

Terms

a(0) =2a(1) =0a(2) =4a(3) =2a(4) =16a(5) =20a(6) =78a(7) =140a(8) =416a(9) =878a(10) =2324a(11) =5280a(12) =13282a(13) =31200a(14) =76724a(15) =182962a(16) =445376a(17) =1069300a(18) =2591118a(19) =6239980a(20) =15089776a(21) =36389278a(22) =87917284a(23) =212144640a(24) =512334722a(25) =1236606720a(26) =2985883684a(27) =7207831202a(28) =17402424496a(29) =42011258900