Binomial Madness

Relevant wiki: Properties of Binomial Coefficients

$\;\;\;\;\displaystyle\binom{16}{0}+\sum_{n = 1}^{16}(2n^2 + 7n - 1)\binom{16}n$
$=\displaystyle 1+\sum_{n=1}^{16}(2n(n-1)+9n-1)\binom{16}n$
$=\displaystyle 1+\sum_{n=1}^{16}(32(n-1)+144)\binom{15}{n-1}-(2^{16}-1)$
$=\displaystyle 2-2^{16}+\sum_{n=1}^{16}(32(n-1))\binom{15}{n-1}+144\times 2^{15}$
$=\displaystyle 2-2^{16}+144\times 2^{15}+\sum_{n=2}^{16}(32(n-1))\binom{15}{n-1}$
$=\displaystyle 2+142\times 2^{15}+\sum_{n=2}^{16}480\binom{14}{n-2}$
$=2+142\times 2^{15}+480\times 2^{14}$
$=2+764\times 2^{14}$
$=12517378$