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A014507
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Number of digraphs with loops, having unlabeled (non-isolated) nodes and n labeled edges.
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19
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1, 2, 13, 162, 3075, 80978, 2784067, 119971162, 6289972169, 392257225754, 28582571639293, 2398695602082442, 229094801646110203, 24652935339990534970, 2963620352166634246995, 395067805289398293647026, 58025593661340099613984593, 9336949406574071339557552946
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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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a(n) = Sum_{k=0..n} Stirling1(n, k)*Bell(2*k). - Vladeta Jovovic, Jun 21 2003
E.g.f.: exp(-1)*Sum_{n>=0} (1+x)^(n^2)/n!. - Paul D. Hanna, Jul 03 2011
a(n) = n!*exp(-1)*Sum_{k>=sqrt(n)} binomial(k^2,n)/k!. - Paul D. Hanna, Jul 03 2011
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MAPLE
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add(combinat[stirling1](n, k)*combinat[bell](2*k), k=0..n) ;
end proc:
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MATHEMATICA
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a[n_] := Sum[StirlingS1[n, k]*BellB[2*k], {k, 0, n}];
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PROG
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{Stirling1(n, k)=n!*polcoeff(binomial(x, n), k)}
{Bell(n)=n!*polcoeff(exp(exp(x+x*O(x^n))-1), n)}
{a(n)=sum(k=0, n, Stirling1(n, k)*Bell(2*k))}
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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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