A037184 Functional digraphs with 1 node not in the image.

6, 48, 420, 3840, 38010, 407904, 4739112, 59405760, 800309070, 11542072080, 177536452236, 2902434644928, 50271450894210, 919799178083520, 17730187503894480, 359183503307677824, 7629999730919490582, 169605272611054951920, 3937616869933172881140

Offset: 3

Author

Erich Friedman

Keywords

• easy
• nonn

Comments

Comment from Christian G. Bower: Labeled graphs where every node has outdegree 1, one node has indegree 0, one node has indegree 2, all other nodes have indegree 1 and there are no loops of length 1.

Crossrefs

A000166 (derangements) gives number of functional digraphs with all nodes in the range, A007778 gives number of functional digraphs with n nodes.

Formula

a(n) = n * ( (n-2)*a(n-1) + (n-1)*a(n-2) ) / (n-3).

E.g.f.: x^3 / ((1-x)^3 * e^x).