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A122193
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Triangle T(n,k) of number of graphs with n labeled vertices and k labeled edges and without isolated vertices, n = 1,.., k = 2..2*n.
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3
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1, 1, 6, 6, 1, 24, 114, 180, 90, 1, 78, 978, 4320, 8460, 7560, 2520, 1, 240, 6810, 63540, 271170, 604800, 730800, 453600, 113400, 1, 726, 43746, 774000, 6075900, 25424280, 61923960, 90720000, 78813000, 37422000, 7484400
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,3
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FORMULA
| E.g.f.: exp(-x)*Sum(exp(binomial(n,2)*y)*x^n/n!,n=0..infinity). Row sums give A055203.
T(n,k) = S_{2,2}(n,k)*k!/2^n; S_{2,2} the generalized Stirling numbers A078739. - Peter Luschny, Mar 25 2011
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EXAMPLE
| 1; 1,6,6; 1,24,114,180,90; 1,78,978,4320,8460,7560,2520; ...
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MAPLE
| # Note that the function implements the full triangle because it can be
# much better reused and referenced in this form.
A122193 := (n, k) -> A078739(n, k)*k!/2^n:
# Displays the truncated triangle from the definition:
seq(print(seq(A122193(n, k), k=2..2*n)), n=1..6); # - Peter Luschny, Mar 25 2011
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CROSSREFS
| Cf. A078739.
Sequence in context: A105817 A093313 A098267 * A098369 A078740 A191504
Adjacent sequences: A122190 A122191 A122192 * A122194 A122195 A122196
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KEYWORD
| easy,nonn,tabf
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 24 2006
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