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A212809
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Decimal expansion of radius of convergence of g.f. for unlabeled trees (A000055).
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1
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3, 3, 8, 3, 2, 1, 8, 5, 6, 8, 9, 9, 2, 0, 7, 6, 9, 5, 1, 9, 6, 1, 1, 2, 6, 2, 5, 7, 1, 7, 0, 1, 7, 0, 5, 3, 1, 8, 3, 7, 7, 4, 6, 0, 7, 5, 3, 2, 9, 6, 7, 7, 9, 5, 5, 7, 2, 3, 0, 3, 7, 7, 6, 2, 5, 7, 6, 6, 6, 0, 5, 0, 1, 8, 9, 6, 2, 0, 7, 6, 6, 5, 6, 3, 5, 2, 8, 7, 9, 8, 3, 6, 7, 3
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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LINKS
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FORMULA
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EXAMPLE
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0.338321856899208...
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MATHEMATICA
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digits = 95; max = 200;
s[n_, k_] := s[n, k] = a[n + 1 - k] + If[n < 2*k, 0, s[n - k, k]];
a[1] = 1;
a[n_] := a[n] = Sum[a[k]*s[n - 1, k]*k, {k, 1, n - 1}]/(n - 1);
A[x_] := Sum[a[k]*x^k, {k, 0, max}];
eq = Log[c] == 1 + Sum[A[c^-k]/k, {k, 2, max}];
r = 1/c /. FindRoot[eq, {c, 3}, WorkingPrecision -> digits + 5];
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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