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A020557
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Number of oriented multigraphs on n labeled arcs (with loops).
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3
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1, 2, 15, 203, 4140, 115975, 4213597, 190899322, 10480142147, 682076806159, 51724158235372, 4506715738447323, 445958869294805289, 49631246523618756274, 6160539404599934652455, 846749014511809332450147, 128064670049908713818925644
(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
| a(n) = Bell(2*n) = A000110(2*n). - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 02 2003
a(n) = EXP(-1)*sum(k=>0, k^(2n)/k!) - Benoit Cloitre (benoit7848c(AT)orange.fr), May 19 2002
E.g.f.: exp(x*(d_z)^2)*(exp(exp(z)-1))|_{z=0}, with the derivative operator d_z := d/dz. Adapted from eqs.(14) and (15) of the 1999 C. M. Bender reference given in A000110.
E.g.f.: exp(-1)*Sum(exp(n^2*x)/n!,n=0..infinity). - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 24 2006
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PROG
| (PARI) for(n=0, 50, print1(ceil(sum(i=0, 1000, i^(2*n)/(i)!)/exp(1)), ", "))
(Other) sage: [bell_number(2*n) for n in xrange(0, 17)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 14 2009]
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CROSSREFS
| Cf. A070906. Bisection of Bell numbers A000110.
Cf. A099977.
Sequence in context: A187655 A046249 A042355 * A184361 A124558 A020565
Adjacent sequences: A020554 A020555 A020556 * A020558 A020559 A020560
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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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