 Nonuniform two-intersecting family bound

On an even ground set $n=2h$, a two-intersecting family has size at most ${\sum }_{j=h+1}^n\left(\genfrac{}{}{0ex}{}{n}{j}\right)$. On an odd ground set $n=2h+1$, the bound is $\left(\genfrac{}{}{0ex}{}{2h}{h+1}\right)+{\sum }_{j=h+2}^n\left(\genfrac{}{}{0ex}{}{n}{j}\right)$. Pair lower levels with complements of upper levels using the intersecting shadow lemma; apply the Erdős-Ko-Rado theorem to the remaining middle level in the odd case.