A072169 Commuting permutations: number of ordered triples of permutations f, g, h in Symm(n) which all commute.

1, 1, 8, 48, 504, 4680, 66240, 856800, 14515200, 242040960, 4775500800, 95520902400, 2175146265600, 50438868480000, 1292330988748800, 34092378448128000, 971277752180736000, 28566680100102144000, 896191466580393984000, 29029508406664077312000

Offset: 0

Author

N. J. A. Sloane, Sep 06 2003. More terms from A061256 from N. J. A. Sloane, Jun 13 2012

Keywords

• nonn

References

• a(1)-a(7) computed by John McKay, Sep 06 2003.

Links

• T. D. Noe, Table of n, a(n) for n = 0..200

Crossrefs

Column k=3 of A362827.

Cf. A061256, A053529.

Programs

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;

Mathematica

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 *)

Formula

Equals A061256(n)*n!.