A138274 Column 2 of triangle A138271; also, column 0 of matrix power A138271^3.
1, 3, 18, 156, 1714, 22368, 333910, 5566728, 101955050, 2027241660, 43372029642, 991507256804, 24084513595722, 618791039789272, 16751222781082878, 476239112549941408, 14179227111187986642, 441017358981919297508
Offset: 0