A126220 Number of binary trees (i.e. rooted trees where each vertex has either 0,1, or 2 children; and, when only one child is present, it is either a right child or a left child ) with n edges and no adjacent vertices of outdegree 2.

1, 2, 5, 14, 40, 116, 344, 1040, 3188, 9880, 30912, 97520, 309856, 990656, 3184672, 10287808, 33379072, 108724864, 355405568, 1165521408, 3833497408, 12642775424, 41799227392, 138512751360, 459973953024, 1530498526208