Number of walks on square lattice. Column y=1 of A052174.

Terms

a(0) =1a(1) =2a(2) =8a(3) =20a(4) =75a(5) =210a(6) =784a(7) =2352a(8) =8820a(9) =27720a(10) =104544a(11) =339768a(12) =1288287a(13) =4294290a(14) =16359200a(15) =55621280a(16) =212751396a(17) =734959368a(18) =2821056160a(19) =9873696560a(20) =38013731756a(21) =134510127752a(22) =519227905728