What is the coefficient of X in the expansion of (x ^ 2 + 3x + 2) ^ 5? （1+X）+（1+X)^2+…… +(1+x)^n=a1+a2x+a2x^2+…… +Anx ^ n, if a1 + A2 + +A (n-1) = 29-n, then what is n?

What is the coefficient of X in the expansion of (x ^ 2 + 3x + 2) ^ 5? （1+X）+（1+X)^2+…… +(1+x)^n=a1+a2x+a2x^2+…… +Anx ^ n, if a1 + A2 + +A (n-1) = 29-n, then what is n?

What is the coefficient of X in the expansion of (x ^ 2 + 3x + 2) ^ 5?
Original formula = (x + 2) ^ 5 (x + 1) ^ 5
In (x + 2) ^ 5, the coefficient of X is 2 ^ 4 * 5 = 80, and the coefficient of constant term is 2 ^ 5 = 32
In (x + 1) ^ 5, the coefficient of X is 5 and the coefficient of constant term is 1
The whole formula x coefficient = 80 * 1 + 32 * 5 = 240
（1+X）+（1+X)^2+…… +(1+x)^n=a1+a2x+a2x^2+…… +Anx ^ n, if a1 + A2 + +A (n-1) = 29-n, then what is n?
a0=1C0+2C0+3C0+4C0+...+nC0
a1=1C1+2C1+3C1+4C1+...+nC1
a2= 2C2+3C2+4C2+...+nC2
a3= 3C3+4C3+...+nC3
...
an= nCn
This should be very clear ~ where A0 = n, an = 1
a0+a1+a2+a3+...+an=2+2^2+2^3+...2^n=2^(n+1)-2
Therefore, a1 + A2 +... + a (n-1) = 2 ^ (n + 1) - 2-a0-an = 2 ^ (n + 1) - 2-n-1 = 2 ^ (n + 1) - 3-N = 29-n
So the solution is n = 4