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
Links
- Nathaniel Johnston, Table of n, a(n) for n = 0..60
Programs
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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
Formula
G.f.: A(x/(1-x)) where A(x) is g.f. for A121933.