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) =5a(4) =7a(5) =20a(6) =35a(7) =83a(8) =161a(9) =355a(10) =720a(11) =1541a(12) =3185a(13) =6733a(14) =14027a(15) =29500a(16) =61663a(17) =129403a(18) =270865a(19) =567911a(20) =1189440a(21) =2492905a(22) =5222449a(23) =10943813a(24) =22928815a(25) =48044900a(26) =100665083a(27) =210927155a(28) =441948689a(29) =926020171