观察下列等式：

$1+2+3+4+\cdots +n=\frac{1}{2}n(n+1);$

$1+3+6+10+\cdots +\frac{1}{2}n(n+1)=\frac{1}{6}n(n+1)(n+2)$;

$1+4+10+20+\cdots +\frac{1}{6}n(n+1)(n+2)=\frac{1}{24}n(n+1)(n+2)(n+3)$;

则有： $1+5+15+35+\cdots \frac{1}{24}n(n+1)(n+2)(n+3)$＝　　．