Convolution triangle by rows, A004736 * (A154108 * 0^(n-k)); row sums = Bell numbers.

Terms

a(0) =1a(1) =2a(2) =0a(3) =3a(4) =0a(5) =2a(6) =4a(7) =0a(8) =4a(9) =7a(10) =5a(11) =0a(12) =6a(13) =14a(14) =27a(15) =6a(16) =0a(17) =8a(18) =21a(19) =54a(20) =114a(21) =7a(22) =0a(23) =10a(24) =28a(25) =81a(26) =228a(27) =523a(28) =8a(29) =0