A381123 Number of unlabeled endofunctions on n points whose self-referencing elements are mapped from another element.

1, 0, 2, 4, 12, 28, 83, 213, 608, 1664, 4703, 13173, 37412, 105995, 302301, 862794, 2470631, 7084425, 20357121, 58573788, 168789684, 486964114, 1406549550, 4066751083, 11769363663, 34090076148, 98820914068, 286672673725, 832183340955, 2417270306657, 7025657374736, 20430883575932, 59444386613999, 173039084438093

Offset: 0

Author

Peter Dolland, Feb 14 2025

Keywords

• nonn

Comments

Equivalently, the number of digraphs on n unlabeled nodes where each node has an out degree 1 and, if it is self-referencing, it is referenced from at least one other node.

Examples

			For n = 2 one node must reference the other one, this one may reference itself or the first one. So a(2) = 2.
For n = 3 there are 7 = A001372(3) endofunctions, but 3 = A001372(2) of them have at least 1 isolated element. So a(3) = 7 - 3 = 4.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Partial differences of A001372.

Formula

a(0) = 1; a(n) = A001372(n) - A001372(n - 1) for n > 0.