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A121063
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Number of labeled directed multigraphs with n arcs for which every vertex has in-degree at least one and out-degree at least one.
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1
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1, 0, 1, 4, 27, 246, 2783, 37424, 582153, 10276452, 202894801, 4429522252, 105943672079, 2754788353526, 77371821493913, 2334279549290960, 75286455363538607, 2584971423426768872, 94138234184851584599, 3624294240897948371036, 147080227272202880297669
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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LINKS
| Nathaniel Johnston, Table of n, a(n) for n = 0..60
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FORMULA
| G.f.: A(x/(1-x)) where A(x) is g.f. for A121933.
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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
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CROSSREFS
| Cf. A052170, A056078, A104209, A121933.
Sequence in context: A181146 A161120 A183430 * A051863 A000699 A138423
Adjacent sequences: A121060 A121061 A121062 * A121064 A121065 A121066
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KEYWORD
| easy,nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 06 2006
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