A069657 Sum( S(n,k) * M(k-1), k=1..n), where S(n,k) = Stirling numbers of the second kind, M(n) = Motzkin numbers, A001006.
0, 1, 2, 6, 24, 115, 628, 3818, 25455, 183968, 1428184, 11824098, 103794727, 961461179, 9360372700, 95448502365, 1016413911387, 11273822075837, 129950445723958, 1553488011957986, 19225242250821071, 245899882175001580, 3245812116097119188, 44155099624566615247
Offset: 0