A061127 Number of degree-n permutations of order exactly 24.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1663200, 19958400, 259459200, 4843238400, 72648576000, 988020633600, 14600749363200, 224704121241600, 3614691131251200, 84808750650624000, 1509309706083379200, 29359195162807910400

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=22;Range[0,nn]!CoefficientList[Series[(Exp[x^24/24]-1)Exp[x+x^2/2+x^3/3+x^4/4+x^6/6+x^8/8+x^12/12]+(Exp[x^12/12]-1)(Exp[x^8/8]-1)Exp[x+x^2/2+x^3/3+x^4/4+x^6/6]+(Exp[x^8/8]-1)(Exp[x^6/6]-1)Exp[x+x^2/2+x^3/3+x^4/4]+(Exp[x^8/8]-1)(Exp[x^3/3]-1)Exp[x+x^2/2+x^4/4],{x,0,nn}],x]//Rest (* Geoffrey Critzer, Feb 04 2013 *)

Formula

E.g.f.: exp(x + 1/2*x^2 + 1/4*x^4) - exp(x + 1/2*x^2 + 1/4*x^4 + 1/8*x^8) - exp(x + 1/2*x^2 + 1/3*x^3 + 1/4*x^4 + 1/6*x^6 + 1/12*x^12) + exp(x + 1/2*x^2 + 1/3*x^3 + 1/4*x^4 + 1/6*x^6 + 1/8*x^8 + 1/12*x^12 + 1/24*x^24).