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) =6a(3) =15a(4) =32a(5) =61a(6) =110a(7) =191a(8) =324a(9) =541a(10) =894a(11) =1467a(12) =2396a(13) =3901a(14) =6338a(15) =10283a(16) =16668a(17) =27001a(18) =43722a(19) =70779a(20) =114560a(21) =185401a(22) =300026a(23) =485495a(24) =785592a(25) =1271161a(26) =2056830a(27) =3328071a(28) =5384984a(29) =8713141