A381121 Number of partially ordered sets ("posets") covering n unlabeled elements.

1, 0, 1, 3, 11, 47, 255, 1727, 14954, 166232, 2384053, 44182143, 1058142319, 32718935706, 1304369332319, 66936884741385, 4414855587293931

Offset: 0

Author

Peter Dolland, Feb 14 2025

Keywords

• nonn
• hard
• more

Examples

			For n = 3 there are 5 posets, but 2 of them have at least 1 unrelated element, so there are 5 - 2 = 3  = a(3) posets without an unrelated element.
		

Crossrefs

Partial differences of A000112.

Formula

a(0) = 1; a(n) = A000112(n) - A000112(n - 1) for n > 0.