Entringer number ($E(n,k)$)

Entringer numbers refine counts of alternating permutations. One standard convention uses $E(0,0)=1$, $E(n,0)=0$ for $n>0$, and $E(n,k)=E(n,k-1)+E(n-1,n-k)$ for $1\le k\le n$. Reversed-row prefix sums generate the triangle.

The Entringer triangle arranges Entringer numbers into rows. Each row is obtained from reversed-row prefix sums, with the boundary convention specified by the recurrence.