Triangle read by rows: T(n,k) is the number of weighted lattice paths B(n) having k uhd strings.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =7a(5) =1a(6) =15a(7) =2a(8) =32a(9) =5a(10) =69a(11) =13a(12) =154a(13) =30a(14) =1a(15) =346a(16) =74a(17) =3a(18) =786a(19) =183a(20) =9a(21) =1806a(22) =449a(23) =28a(24) =4180a(25) =1114a(26) =78a(27) =1a(28) =9745a(29) =2767