A027101 a(n) = diagonal sum of right justified array T given by A027082.

1, 1, 3, 9, 18, 49, 127, 331, 883, 2376, 6439, 17591, 48347, 133589, 370883, 1033997, 2893498, 8124303, 22880569, 64616728, 182943204, 519146325, 1476337528, 4206621803, 12008000771, 34335363519, 98332343337, 282026580873