The value of the sum ${C_1} + 2{C_2} + 3{C_3} + 4{C_4} + .... + n{C_n}$ is equal to:

$\binom{50}{4} + \sum_{i=1}^{6} \binom{56-i}{3} = \dots$

The value of $-{ }^{15}C_{1} 2 \cdot { }^{15}C_{2} - 3 \cdot { }^{15}C_{3} \ldots - 15 \cdot { }^{15}C_{15} { }^{14}C_{1} { }^{14}C_{3} { }^{14}C_{5} \ldots { }^{14}C_{11}$ is

$^nC_0 - \frac{1}{2} ^nC_1 + \frac{1}{3} ^nC_2 - \dots + (-1)^n \frac{^nC_n}{n+1} = $

$\binom{47}{4} + \sum_{r=1}^5 \binom{52-r}{3} = \dots$

If $(1+x-2x^2)^6 = 1+a_1x+a_2x^2+\ldots+a_{12}x^{12}$, then the value of $a_2+a_4+a_6+\ldots+a_{12}$ is