Stirling-like number triangle defined by paired decomposition of C(n+3,3) = A000292.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =4a(5) =1a(6) =1a(7) =12a(8) =10a(9) =1a(10) =1a(11) =32a(12) =67a(13) =20a(14) =1a(15) =1a(16) =80a(17) =376a(18) =252a(19) =35a(20) =1a(21) =1a(22) =192a(23) =1909a(24) =2560a(25) =742a(26) =56a(27) =1a(28) =1a(29) =448