$\dfrac{d^{(n)}}{{dx}^{(n)}} \sin(x^2) |_{x=0}= \left \{
\begin{array}{ll}
(-1)^n \dfrac{(4n+2)!}{(2n+1)!}~:n=(4k+2), k=0,1,2, \dots 24 \\
0~:~ \text{else}
\end{array}\right.$
https://oeis.org/A024343
$\dfrac{d^{(n)}}{{dx}^{(n)}} \sin(x^2) |_{x=0}= \left \{
\begin{array}{ll}
(-1)^n \dfrac{(4n+2)!}{(2n+1)!}~:n=(4k+2), k=0,1,2, \dots 24 \\
0~:~ \text{else}
\end{array}\right.$
https://oeis.org/A024343