0,1

Inverse binomial transform of A114491.

This sequence enumerates a certain type of matroid, except for the first entry (which is 2 instead of 1). If the first entry is changed from 2 to 1, giving A118085, this enumerates "combinatorial geometries" on n labeled points.

These are matroids in which no element has rank 0; equivalently, all one-element sets are independent; equivalently, the closure of the empty set is empty.

These are called "simple matroids" in A002773. So A118085 is the "labeled" equivalent of that sequence, which counts unlabeled points.

For all n>1, a function like "x2" is counted in A114491 but not in the present sequence.

Cf. A114302, A114303, A114491, A118085, A002773.

Sequence in context: A032163 A038078 A000139 this_sequence A052621 A131057 A051852

Adjacent sequences: A114569 A114570 A114571 this_sequence A114573 A114574 A114575

nonn

D. E. Knuth, Aug 17 2008, Oct 14 2008