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A322661
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Number of graphs with loops spanning n labeled vertices.
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68
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1, 1, 5, 45, 809, 28217, 1914733, 254409765, 66628946641, 34575388318705, 35680013894626133, 73392583417010454429, 301348381381966079690489, 2471956814761996896091805993, 40530184362443281653842556898237, 1328619783326799871943604598592805525
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OFFSET
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0,3
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COMMENTS
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The span of a graph is the union of its edges.
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LINKS
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FORMULA
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Inverse binomial transform of A006125(n+1) = 2^binomial(n+1,2).
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EXAMPLE
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The a(2) = 5 edge-sets:
{{1,2}}
{{1,1},{1,2}}
{{1,1},{2,2}}
{{1,2},{2,2}}
{{1,1},{1,2},{2,2}}
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MATHEMATICA
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Table[Sum[(-1)^(n-k)*Binomial[n, k]*2^Binomial[k+1, 2], {k, 0, n}], {n, 10}]
(* second program *)
Table[Select[Expand[Product[1+x[i]*x[j], {j, n}, {i, j}]], And@@Table[!FreeQ[#, x[i]], {i, n}]&]/.x[_]->1, {n, 7}]
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PROG
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(PARI) a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n, k)*2^binomial(k+1, 2)) \\ Andrew Howroyd, Jan 06 2024
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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