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A369289
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Number of connected graphs with loops (symmetric relations) on n unlabeled vertices with at most n edges.
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3
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1, 2, 2, 4, 8, 17, 39, 92, 227, 573, 1482, 3883, 10343, 27786, 75392, 205933, 566166, 1564316, 4342431, 12100382, 33836606, 94903889, 266914438, 752517020, 2126292931, 6020035120, 17075411671, 48514471709, 138051863755, 393397897262, 1122523343690
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OFFSET
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0,2
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COMMENTS
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The graphs considered here can have loops but not parallel edges.
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LINKS
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FORMULA
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Inverse Euler transform of A369145.
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PROG
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(PARI) \\ TreeGf gives gf of A000081.
TreeGf(N)={my(A=vector(N, j, 1)); for (n=1, N-1, A[n+1] = 1/n * sum(k=1, n, sumdiv(k, d, d*A[d]) * A[n-k+1] ) ); x*Ser(A)}
seq(n)={my(t=TreeGf(n)); my(g(e)=subst(t + O(x*x^(n\e)), x, x^e) + O(x*x^n)); Vec(1 + (sum(d=1, n, eulerphi(d)/d*log(1/(1-g(d)))) + ((1+g(1))^2/(1-g(2))-1)/2 + 2*g(1) - 2*g(1)^2 )/2) }
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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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