asymptotic formula for A006531 ?

[Detlef Pauly]

Anybody got a (nice) asymptotic formula for A006531 ?

A006531: sum( S(n,k) * k! * M(k-1), k=1..n),

S(n,k): Stirling number of the second kind,
M(n): Motzkin number, A001006.

DETLEF PAULY
dp at dettodet.de