Sorry if this is well known to those who well know it, but the following seem not to be in OEIS: 1, 1, 2, 7, 35, 191, 1304, ... 1, 2, 5, 18, 89, 492, 3359, ... Presumably because I've made a stupid mistake in my hand clculations. They are the numerators and denominators of the convergents to the negative continued fraction 1 - 1/(2 - 1/(3 - 1/(4 - ...))) R.