A121063 Number of labeled directed multigraphs with n arcs for which every vertex has in-degree at least one and out-degree at least one.

1, 0, 1, 4, 27, 246, 2783, 37424, 582153, 10276452, 202894801, 4429522252, 105943672079, 2754788353526, 77371821493913, 2334279549290960, 75286455363538607, 2584971423426768872, 94138234184851584599, 3624294240897948371036, 147080227272202880297669

Offset

0,4

Links

Nathaniel Johnston, Table of n, a(n) for n = 0..60

Formula

G.f.: A(x/(1-x)) where A(x) is g.f. for A121933.

Maple

n:=20: t:=taylor(sum(sum((-1)^(s-k)*binomial(s, k)*((1+x/(1-x))^(k-1)-1)^k*((1+x/(1-x))^k-1)^(s-k), k=0..s), s=0..n), x, n+1): seq(coeff(t, x, s), s=0..n); # Nathaniel Johnston, Apr 28 2011

Crossrefs

Cf. A052170, A056078, A104209, A121933.

Sequence in context: A183430 A212559 A265268 * A229619 A051863 A000699

Adjacent sequences: A121060 A121061 A121062 * A121064 A121065 A121066

Keyword

easy,nonn

Author

Vladeta Jovovic, Sep 06 2006

Status

approved