Multi-bifurcating recursion of a factorial type based on the Eulerian numbers A008292 as a triangle sequence: t(n,k) = Sum_{j=0..k+1} (-1)^j * binomial(n + 1, j)*(k + 1 - j)^n; f(n, m) = If[m <= floor(n/2), f(m, 1)*f(n - m, 1)*t(n + 1, m)].

A155556

Multi-bifurcating recursion of a factorial type based on the Eulerian numbers A008292 as a triangle sequence: t(n,k) = Sum_{j=0..k+1} (-1)^j * binomial(n + 1, j)*(k + 1 - j)^n; f(n, m) = If[m <= floor(n/2), f(m, 1)*f(n - m, 1)*t(n + 1, m)].