If \({\left({}^{30}C_{1}\right)}^{2}+2{\left({}^{30}C_{2}\right)}^{2}+3{\left({}^{30}C_{3}\right)}^{2}+\ldots ..+30{\lef…

If \({\left({}^{30}C_{1}\right)}^{2}+2{\left({}^{30}C_{2}\right)}^{2}+3{\left({}^{30}C_{3}\right)}^{2}+\ldots ..+30{\left({}^{30}C_{30}\right)}^{2}\)\(=\frac{\alpha \cdot 60!}{(30!{)}^{2}}\),then \(\alpha\) is equal to

[JEE Main 2023, 24 Jan (Shift 2)]