Identity

A + B(x + 1) + C(x + 1)^2 + D(x + 1)^3 + E(x + 1)^4 + F(x + 1)^5
=A+Bx+B+Cx^2+2Cx+C+Dx^3+3Dx^2+3Dx+D+Ex^4+4Ex^3+6Ex^2+4Ex+E
+Fx^5+5Fx^4+10Fx^3+10Fx^2+5Fx+F
=(A+B+C+D+E+F)+(B+2C+3D+4E+5F)x+(C+3D+6E+10F)x^2
+(D+4E+10F)x^3+(E+5F)x^4+Fx^5
obviously,F=2
E+5F=3
E=-7
D+4E+10F=-1
D=7
C+3D+6E+10F=3
C=4
B+2C+3D+4E+5F=-5
B=-16
A+B+C+D+E+F=7
A=17