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A309313
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Number of simple labeled graphs on 2n nodes with exactly n connected components that are trees or cycles.
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2
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1, 1, 19, 540, 23597, 1381695, 101682724, 9016296289, 935625630797, 111226656560877, 14903545528332565, 2222230881719482634, 364942065096639623872, 65448490334085989020670, 12726830901257817750060165, 2667188536603107740647377075, 599286881811684624273478547325
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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MAPLE
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b:= proc(n, k) option remember; `if`(k<0 or k>n, 0,
`if`(n=0, 1, add(binomial(n-1, i)*b(n-1-i, k-1)*
`if`(i<2, 1, i!/2 +(i+1)^(i-1)), i=0..n-k)))
end:
a:= n-> b(2*n, n):
seq(a(n), n=0..20);
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MATHEMATICA
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b[n_, k_] := b[n, k] = If[k < 0 || k > n, 0,
If[n == 0, 1, Sum[Binomial[n - 1, i]*b[n - 1 - i, k - 1]*
If[i<2, 1, i!/2 + (i+1)^(i-1)], {i, 0, n-k}]]];
a[n_] := b[2n, n];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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