Staircase on Pascal's triangle.

Terms

a(0) =1a(1) =3a(2) =10a(3) =20a(4) =70a(5) =126a(6) =462a(7) =792a(8) =3003a(9) =5005a(10) =19448a(11) =31824a(12) =125970a(13) =203490a(14) =817190a(15) =1307504a(16) =5311735a(17) =8436285a(18) =34597290a(19) =54627300a(20) =225792840a(21) =354817320a(22) =1476337800a(23) =2310789600a(24) =9669554100a(25) =15084504396a(26) =63432274896a(27) =98672427616a(28) =416714805914a(29) =646626422970