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A001433
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Number of graphs with n nodes and n-1 edges.
(Formerly M2588 N1024)
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9
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1, 1, 1, 3, 6, 15, 41, 115, 345, 1103, 3664, 12763, 46415, 175652, 691001, 2821116, 11932174, 52211412, 236007973, 1100528508, 5287050500, 26134330813, 132760735671, 692294900849, 3701754158688, 20275893222445, 113657560920970, 651449039159673, 3814790900995022, 22805438484189851
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OFFSET
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1,4
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REFERENCES
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J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 146.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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MATHEMATICA
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Needs["Combinatorica`"]
(* Second program (not needing Combinatorica): *)
permcount[v_] := Module[{m = 1, s = 0, k = 0, t}, For[i = 1, i <= Length[v], i++, t = v[[i]]; k = If[i > 1 && t == v[[i - 1]], k + 1, 1]; m *= t*k; s += t]; s!/m];
edges[v_, t_] := Product[Product[g = GCD[v[[i]], v[[j]]]; t[v[[i]]* v[[j]]/g]^g, {j, 1, i - 1}], {i, 2, Length[v]}]*Product[c = v[[i]]; t[c]^Quotient[c - 1, 2]*If[OddQ[c], 1, t[c/2]], {i, 1, Length[v]}];
a[n_] := a[n] = Module[{s = 0}, Do[s += permcount[p]*edges[p, 1 + x^# &], {p, IntegerPartitions[n]}]; s/n!] // Expand // SeriesCoefficient[#, {x, 0, n-1}]&;
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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