STATUS
reviewed
approved
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Revision History for A001433
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
STATUS
proposed
reviewed
STATUS
editing
proposed
MATHEMATICA
Needs["Combinatorica`"]
(* first do *) Needs["Combinatorica`"] (* then *) Table[ NumberOfGraphs[n, n-1], {n, 1, 25}] (* Robert G. Wilson v *)
STATUS
proposed
editing
STATUS
editing
proposed
MATHEMATICA
Table[Print[n, " ", a[n]]; a[n], {n, 1, 3035}] (* Jean-François Alcover, Aug 18 2022, after Andrew Howroyd in A008406 *)
MATHEMATICA
Table[Print[n, " ", a[n]]; a[n], {n, 1, 30}] (* Jean-François Alcover, Aug 18 2022, after Andrew Howroyd in A008406 *)
EXTENSIONS
a(26)-a(30) from Jean-François Alcover, Aug 18 2022
DATA
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
MATHEMATICA
(* 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}]&;
Table[Print[n, " ", a[n]]; (* Jean-François Alcover, Aug 18 2022, after Andrew Howroyd in A008406 *)
EXTENSIONS
a(26)-a(30) from Jean-François Alcover, Aug 18 2022
STATUS
approved
editing
STATUS
editing
approved