A192251 1-sequence of reduction of central binomial coefficient sequence by x^2 -> x+1.

0, 2, 8, 48, 258, 1518, 8910, 53526, 323796, 1976876, 12138456, 74921904, 464320368, 2887660168, 18011618368, 112633305568, 705899650498, 4432668783838, 27882818399038, 175661366346838, 1108193133814138, 6999963827434378, 44265660573879298