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

3,1

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.

Links

Table of n, a(n) for n=3..21.

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).

Crossrefs

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

Sequence in context: A258790 A345077 A244038 * A179075 A175916 A231104

Adjacent sequences: A037181 A037182 A037183 * A037185 A037186 A037187

Keyword

easy,nonn

Author

Erich Friedman

Status

approved