A114572 Number of "ultrasweet" Boolean functions of n variables which depend on all the variables.

2, 1, 2, 6, 27, 185, 2135, 55129

Offset

0,1

Comments

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.

Links

Table of n, a(n) for n=0..7.

Example

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

Crossrefs

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

Sequence in context: A038078 A000139 A302190 * A052621 A212671 A131057

Adjacent sequences: A114569 A114570 A114571 * A114573 A114574 A114575

Keyword

nonn

Author

Don Knuth, Aug 17 2008, Oct 14 2008

Status

approved