Constant term of the reduction by x^2 -> x+1 of the polynomial p(n,x) defined below in Comments.

Terms

a(0) =2a(1) =0a(2) =5a(3) =1a(4) =18a(5) =13a(6) =81a(7) =106a(8) =413a(9) =729a(10) =2258a(11) =4653a(12) =12833a(13) =28666a(14) =74493a(15) =173545a(16) =437346a(17) =1041421a(18) =2583089a(19) =6221322a(20) =15304541a(21) =37079289a(22) =90826994a(23) =220729069a(24) =539487297a(25) =1313161498a(26) =3205831869a(27) =7809748489a(28) =19054635650a(29) =46439068365