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A072169
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Commuting permutations: number of ordered triples of permutations f, g, h in Symm(n) which all commute.
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5
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1, 1, 8, 48, 504, 4680, 66240, 856800, 14515200, 242040960, 4775500800, 95520902400, 2175146265600, 50438868480000, 1292330988748800, 34092378448128000, 971277752180736000, 28566680100102144000, 896191466580393984000, 29029508406664077312000
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OFFSET
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0,3
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REFERENCES
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a(1)-a(7) computed by John McKay, Sep 06 2003.
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LINKS
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FORMULA
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MATHEMATICA
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nn = 20; b = Table[DivisorSigma[1, n], {n, nn}]; Range[0, nn]! CoefficientList[Series[Product[1/(1 - x^m)^b[[m]], {m, nn}], {x, 0, nn}], x] (* T. D. Noe, Jun 19 2012 *)
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PROG
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(Magma) for n in {1 .. 5} do G := SymmetricGroup(n); t1 := 0; for g in G do for h in G do for i in G do if g*h eq h*g and g*i eq i*g and h*i eq i*h then t1 := t1+1; end if; end for; end for; end for; n, t1; end for;
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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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