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A098622
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Consider the family of multigraphs enriched by the species of partitions. Sequence gives number of those multigraphs with n loops and arcs.
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1
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1, 2, 17, 250, 5465, 162677, 6241059, 297132409, 17075153860, 1159545515804, 91501467848088, 8276847825732141, 848577193578286942, 97672164219292005480, 12518933902769241287267, 1774279753092963892540493
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Alternatively, consider the family of multigraphs enriched by the species of involutions. Sequence also gives number of those multigraphs with n loops and arcs.
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REFERENCES
| G. Paquin, D\'enombrement de multigraphes enrichis, M\'emoire, Math. Dept., Univ. Qu\'ebec \`a Montr\'eal, 2004.
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FORMULA
| E.g.f.: exp(-1)*Sum(exp(n^2*(exp(x)-1))/n!,n=0..infinity). - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 24 2006
a(n) = Sum_{k=0..n} Stirling2(n,k)*Bell(2*k). - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 24 2006
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CROSSREFS
| Sequence in context: A036082 A099694 A099698 * A020561 A099702 A029735
Adjacent sequences: A098619 A098620 A098621 * A098623 A098624 A098625
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Oct 26 2004
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 24 2006
Edited by N. J. A. Sloane (njas(AT)research.att.com) at the suggestion of Andrew Plewe, Jun 15 2007
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