h:= proc(l) local n; n:=nops(l); add(i, i=l)! /mul(mul(1+l[i]-j
+add(`if`(l[k]>=j, 1, 0), k=i+1..n), j=1..l[i]), i=1..n)
end:
g:= (n, i, l)-> `if`(n=0 or i=1, h([l[], 1$n])^2, `if`(i<1, 0,
add(g(n-i*j, i-1, [l[], i$j]), j=0..n/i))):
a:= n-> n! -g(n, 6, []):
# Alternative:
a:= proc(n) option remember; `if`(n<7, 0, `if`(n=7, 1, ((-93464*n+1072*n^4
+72128-125284*n^2+84*n^6+994*n^5-30491*n^3+n^7) *a(n-1)
-4*(14*n^5+399*n^4+1124*n^3-7354*n^2-23983*n-5042)*(n-1)^2 *a(n-2)
+4*(-7359-2629*n+1596*n^2+196*n^3)*(n-1)^2*(n-2)^2 *a(n-3)
-1152*(1+2*n)*(n-1)^2*(n-2)^2*(n-3)^2 *a(n-4))/
((n-7)*(n+9)*(n+8)^2*(n+5)^2)))
end:
