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A346498
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Irregular triangular array read by rows. T(n,k) is the number of n X n matrices over GF(2) whose characteristic polynomial has exactly k distinct irreducible factors.
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0
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2, 10, 6, 176, 336, 14016, 44800, 6720, 4032512, 22220800, 7301120, 6213763072, 37056675840, 25449037824, 32018926665728, 264750395031552, 250575870492672, 15604761231360, 870713558978002944, 6977650241843494912, 9453579320929812480, 1144800951958241280
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OFFSET
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1,1
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LINKS
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EXAMPLE
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2,
10, 6,
176, 336,
14016, 44800, 6720,
4032512, 22220800, 7301120,
6213763072, 37056675840, 25449037824
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MATHEMATICA
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nn = 8; q = 2; b[p_, i_] := Count[p, i]; d[p_, i_] := Sum[j b[p, j], {j, 1, i}] + i Sum[b[p, j], {j, i + 1, Total[p]}]; aut[deg_, p_] := Product[Product[
q^(d[p, i] deg) - q^((d[p, i] - k) deg), {k, 1, b[p, i]}], {i, 1,
Total[p]}]; A001037 = Table[1/n Sum[MoebiusMu[n/d] q^d, {d, Divisors[n]}], {n, 1, nn}]; g[u_, v_, deg_] := Total[Map[v u^(deg Total[#])/aut[deg, #] &, Level[Table[IntegerPartitions[n], {n, 0, nn}], {2}]]] - v + 1; Map[Select[#, # > 0 &] &, Drop[Table[Product[q^n - q^i, {i, 0, n - 1}], {n, 0, nn}]CoefficientList[
Series[Apply[Times, Table[g[u, v, deg]^A001037[[deg]], {deg, 1, nn}]], {u, 0,
nn}], {u, v}], 1]] // Grid
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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