A088814 Matrix product of unsigned Lah-triangle |A008297(n,k)| and Stirling2-triangle A008277(n,k).

1, 3, 1, 13, 9, 1, 73, 79, 18, 1, 501, 755, 265, 30, 1, 4051, 7981, 3840, 665, 45, 1, 37633, 93135, 57631, 13580, 1400, 63, 1, 394353, 1192591, 911582, 274141, 38290, 2618, 84, 1, 4596553, 16645431, 15285313, 5633922, 999831, 92358, 4494, 108, 1, 58941091