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A020565
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Number of cyclic oriented multigraphs on n labeled arcs (with loops).
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1
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1, 2, 15, 205, 4202, 118096, 4300364, 195155304, 10727473182, 698874420944, 53040545101942, 4624423933685370, 457851029540848580, 50977215595819988320, 6329927203532081983976, 870296461701522595081624, 131659595370255359745290076
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OFFSET
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0,2
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REFERENCES
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G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.
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LINKS
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FORMULA
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E.g.f.: Sum(Bell(2*n)*log(1-log(1-x))^n/n!, n=0..infinity). - Vladeta Jovovic, May 02 2004
E.g.f.: exp(-1)*Sum((1-log(1-x))^(n^2)/n!,n=0..infinity). - Vladeta Jovovic, Mar 04 2008
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MAPLE
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add((-1)^(n-k)*combinat[stirling1](n, k)*A014507(k), k=0..n) ;
end proc:
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MATHEMATICA
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b[n_] := Sum[StirlingS1[n, k]*BellB[2*k], {k, 0, n}];
a[n_] := Sum[(-1)^(n-k)*StirlingS1[n, k]*b[k], {k, 0, n}];
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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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