The initial terms of the binomial transform of the n-th row of triangle A091063 forms the n-th row of triangle A059438 transposed (permutations of [1..n] with k components); the row sums of A059438 equal the factorials.
FORMULA
G.f.: A(x) = 1/(1-x*g(x)) where g(x) is the g.f. of A075834 shift 1 place left.