# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a121063 Showing 1-1 of 1 %I A121063 #8 Feb 06 2019 00:36:40 %S A121063 1,0,1,4,27,246,2783,37424,582153,10276452,202894801,4429522252, %T A121063 105943672079,2754788353526,77371821493913,2334279549290960, %U A121063 75286455363538607,2584971423426768872,94138234184851584599,3624294240897948371036,147080227272202880297669 %N 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. %H A121063 Nathaniel Johnston, Table of n, a(n) for n = 0..60 %F A121063 G.f.: A(x/(1-x)) where A(x) is g.f. for A121933. %p A121063 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 %Y A121063 Cf. A052170, A056078, A104209, A121933. %K A121063 easy,nonn %O A121063 0,4 %A A121063 _Vladeta Jovovic_, Sep 06 2006 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE