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A053598
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Number of n-node unlabeled digraphs without isolated nodes.
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6
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1, 0, 2, 13, 202, 9390, 1531336, 880492496, 1792477159408, 13026163465206704, 341247403996148180800, 32522568124623933138617088, 11366712907916015518547782806784, 14669074325967499043636521641422216704, 70315641946149306808455637518883828774996992
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OFFSET
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0,3
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COMMENTS
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Equals first differences of A000273.
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LINKS
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FORMULA
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MAPLE
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b:= proc(n, i, l) `if`(n=0 or i=1, 1/n!*2^((p-> add(p[j]-1+add(
igcd(p[k], p[j]), k=1..j-1)*2, j=1..nops(p)))([l[], 1$n])),
add(b(n-i*j, i-1, [l[], i$j])/j!/i^j, j=0..n/i))
end:
a:= n-> b(n$2, [])-`if`(n=0, 0, b(n-1$2, [])):
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MATHEMATICA
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Needs["Combinatorica`"];
nn=15; s=Sum[NumberOfDirectedGraphs[n]x^n, {n, 0, nn}]; CoefficientList[Series[s (1-x), {x, 0, nn}], x] (* Geoffrey Critzer, Oct 09 2012 *)
Join[{1}, Table[GraphPolynomial[n, x, Directed] /. x -> 1, {n, 0, 15}] // Differences] (* Jean-François Alcover, Feb 04 2015 *)
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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STATUS
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approved
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