Let Sn be the set of all permutations of [n] = { 1 , … , n} and let W be the subset consisting of permutations σ∈ Sn avoiding 132 and 312-patterns. The monomial ideal IW=〈xσ=∏i=1nxiσ(i):σ∈W〉 in the polynomial ring R= k[x1, … , xn] over a field k is called a hypercubic ideal in Kumar and Kumar (Proc. Indian Acad. Sci. (Math Sci.)126(4) (2016) 479–500). The Alexander dual IW[n] of IW with respect to n= (n, … , n) has the minimal cellular resolution supported on the first barycentric subdivision Bd(Δ n-1) of an n- 1 -simplex Δ n-1. We show that the number of standard monomials of the Artinian quotient RIW[n] equals the number of rooted-labelled unimodal forests on the vertex set [n]. In other words, dimk(RIW[n])=∑r=1nr!s(n,r)=Per([mij]n×n),where s(n, r) is the (signless) Stirling number of the first kind and Per([mij]n×n) is the permanent of the matrix [mij] with mii= i and mij= 1 for i≠ j. For various subsets S of Sn consisting of permutations avoiding patterns, the corresponding integer sequences {dimk(RIS[n])}n=1∞ are identified.