A381089 Number of binary relations on n unlabeled points without isolated points.

1, 0, 7, 86, 2846, 285984, 96348100, 112089342912, 458072631172864, 6665705090236713408, 349377212708652631367712, 66602723210653815331014240512, 46557323276092409455163109412993536, 120168498152266645852126063743794842575872

Offset

0,3

Comments

Equivalently, the number of simple digraphs on n unlabeled two-colored nodes where each node is connected to at least one other node.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..50

Formula

a(n) = A000595(n) - Sum_{i=1..n} (i+1)*a(n-i).

Example

For n = 2 there are 10 (=A000595(2)) - 3 (=number of relations with isolated points) = 7 = a(2) relations.
For n = 3 there are 104 (=A000595(3)) - 2 * 7 (=number of relations with exactly one isolated point) - 3 * 0 (=number of relations with exactly two isolated points) - 4 * 1 (=number of relations with exactly three isolated points) = 86 = a(3) relations.

Crossrefs

Cf. A000595.

Sequence in context: A220306 A344106 A346987 * A092586 A048363 A254473

Adjacent sequences: A381086 A381087 A381088 * A381090 A381091 A381092

Keyword

nonn

Author

Peter Dolland, Feb 13 2025

Status

approved