Triangle of third-order Eulerian numbers: 3-Stirling permutations enumerated by ascents.

Terms

a(0) =1a(1) =1a(2) =3a(3) =1a(4) =12a(5) =15a(6) =1a(7) =33a(8) =141a(9) =105a(10) =1a(11) =78a(12) =786a(13) =1830a(14) =945a(15) =1a(16) =171a(17) =3450a(18) =17538a(19) =26685a(20) =10395a(21) =1a(22) =360a(23) =13257a(24) =125352a(25) =396495a(26) =435960a(27) =135135a(28) =1a(29) =741