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A215864
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Number of simple labeled graphs on n+4 nodes with exactly n connected components that are trees or cycles.
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2
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0, 137, 1267, 6412, 23597, 70707, 183099, 424809, 904299, 1795794, 3367364, 6017011, 10318126, 17075786, 27395466, 42765846, 65157498, 97139343, 142014873, 203980238, 288306403, 401547685, 551779085, 748864935, 1004761485, 1333856160, 1753346322, 2283660477
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: (7*x^3+59*x^2-34*x-137)*x/(x-1)^9.
a(n) = C(n+4,5)*(15*n^3+390*n^2+2285*n+3886)/48.
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MAPLE
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a:= n-> binomial(n+4, 5)*(3886+(2285+(390+15*n)*n)*n)/48:
seq(a(n), n=0..40);
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MATHEMATICA
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CoefficientList[Series[(7x^3+59x^2-34x-137)x/(x-1)^9, {x, 0, 30}], x] (* Harvey P. Dale, Jul 18 2019 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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