A061121 Number of degree-n permutations of order exactly 6.

0, 0, 0, 0, 20, 240, 1470, 10640, 83160, 584640, 4496030, 42658440, 371762820, 3594871280, 38650622010, 396457108320, 4330689250160, 53963701424640, 641211774798510, 8205894865096280, 113786291585124060

Offset: 1

Author

Vladeta Jovovic, Apr 14 2001

Keywords

• easy
• nonn

Crossrefs

Cf. A000085, A001470, A001472, A052501, A053496-A053505, A001189, A001471, A001473, A061121-A061128.

Programs

Mathematica

nn=21;Range[0,nn]!CoefficientList[Series[(Exp[x^6/6]-1)Exp[x+x^2/2+x^3/3]+(Exp[x^2/2]-1)(Exp[x^3/3]-1)Exp[x],{x,0,nn}],x]//Rest  (* Geoffrey Critzer, Feb 04 2013 *)

Formula

E.g.f.: exp(x)-exp(x+1/2*x^2)-exp(x+1/3*x^3)+exp(x+1/2*x^2+1/3*x^3+1/6*x^6).