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

Terms

a(0) =0a(1) =1a(2) =1a(3) =6a(4) =9a(5) =31a(6) =60a(7) =169a(8) =369a(9) =954a(10) =2201a(11) =5479a(12) =12960a(13) =31721a(14) =75881a(15) =184326a(16) =443169a(17) =1072871a(18) =2585340a(19) =6249329a(20) =15074649a(21) =36413754a(22) =87877681a(23) =212208719a(24) =512231040a(25) =1236774481a(26) =2985612241a(27) =7208270406a(28) =17401713849a(29) =42012408751