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A020561
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Number of ordered oriented multigraphs on n labeled arcs (with loops).
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1
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1, 2, 17, 252, 5535, 165278, 6355147, 303080956, 17440307953, 1185613611362, 93640428880873, 8476453909912332, 869565923845396207, 100138764123162257470, 12840593975018953569971, 1820531766301308581051116, 283643668353734597645391393
(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} abs(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>=0} binomial(k^2 + n-1,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, abs(Stirling1(n, k))*Bell(2*k))}
(PARI) {a(n)=round(n!*exp(-1)*suminf(k=0, binomial(k^2 + n-1, n)/k!))} /* Paul D. Hanna */
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CROSSREFS
| Sequence in context: A099694 A099698 A098622 * A099702 A029735 A037896
Adjacent sequences: A020558 A020559 A020560 * A020562 A020563 A020564
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KEYWORD
| nonn
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AUTHOR
| Gilbert Labelle (gilbert(AT)lacim.uqam.ca), Simon Plouffe (simon.plouffe(AT)gmail.com)
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