The numbers of this sequence are calculated by
binomial (2n,n) - n
where n is the number of the member.
n=1: binomial (2,1) - 1 = 2!/(1!1!) - 1 = 2 - 1 = 1
n=2: binomial (4,2) - 2 = 4!/(2!2!) - 2 = 6 - 2 = 4
n=3: binomial (6,3) - 3 = 6!/(3!3!) - 3 = 20 - 3 = 17
n=4: binomial (8,4) - 4 = 8!/(4!4!) - 4 = 70 - 4 = 66
n=5: binomial (10,5) - 5 = 10!/(5!5!) - 5 = 252 - 5 = 247
n=6: binomial (12,6) - 6 = 12!/(6!6!) - 6 = 924 - 6 = 918
n=7: binomial (14,7) - 7 = 14!/(7!7!) - 7 = 3432 - 7 = 3425
n=8: binomial (16,8) - 8 = 16!/(8!8!) - 8 = 12870 - 8 = 12862