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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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2
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1, 2, 13, 162, 3075, 80978, 2784067, 119971162, 6289972169, 392257225754, 28582571639293, 2398695602082442, 229094801646110203, 24652935339990534970, 2963620352166634246995
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| G. Labelle, Counting enriched multigraphs..., Discrete Math., 217 (2000), 237-248.
G. Paquin, D\'enombrement de multigraphes enrichis, M\'emoire, Math. Dept., Univ. Qu\'ebec \`a Montr\'eal, 2004.
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FORMULA
| Sum_{k=0..n} Stirling1(n, k)*Bell(2*k). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 21 2003
E.g.f.: exp(-1)*Sum_{n>=0} (1+x)^(n^2)/n!. [From Paul D. Hanna, Jul 3 2011]
a(n) = n!*exp(-1)*Sum_{k>=sqrt(n)} binomial(k^2,n)/k!. [From Paul D. Hanna, Jul 3 2011]
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PROG
| (PARI) /* From Vladeta Jovovic's formula: */
{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
| Sequence in context: A054382 A062593 A192563 * A132614 A187927 A098638
Adjacent sequences: A014504 A014505 A014506 * A014508 A014509 A014510
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KEYWORD
| nonn
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AUTHOR
| Simon Plouffe, gilbert(AT)lacim.uqam.ca (Gilbert Labelle).
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