Triangle read by rows: matrix 4th power of the Stirling2 triangle A008277.

Terms

a(0) =1a(1) =4a(2) =1a(3) =22a(4) =12a(5) =1a(6) =154a(7) =136a(8) =24a(9) =1a(10) =1304a(11) =1650a(12) =460a(13) =40a(14) =1a(15) =12915a(16) =21904a(17) =8550a(18) =1160a(19) =60a(20) =1a(21) =146115a(22) =318521a(23) =162904a(24) =30590a(25) =2450a(26) =84a(27) =1a(28) =1855570a(29) =5051988