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

Terms

a(0) =0a(1) =1a(2) =1a(3) =8a(4) =11a(5) =45a(6) =80a(7) =251a(8) =517a(9) =1432a(10) =3195a(11) =8317a(12) =19360a(13) =48827a(14) =116213a(15) =288360a(16) =694331a(17) =1708397a(18) =4138480a(19) =10138363a(20) =24636645a(21) =60217912a(22) =146570491a(23) =357833309a(24) =871703360a(25) =2126857275a(26) =5183425493a(27) =12642971912a(28) =30819571387a(29) =75160150861