A326242 Number of degree-n odd permutations of order dividing 12.
0, 0, 1, 3, 12, 60, 360, 2016, 11088, 73872, 602640, 4411440, 81677376, 934435008, 8100473472, 104370819840, 1448725616640, 15823660179456, 247231858514688, 3703908371910912, 66727356304757760, 1124506454958351360, 19305439846610835456
Offset: 0
Keywords
Examples
For n=3 the a(3)=3 solutions are (1, 2), (2, 3), (1, 3) (permutations in cyclic notation).
Links
- Robert Israel, Table of n, a(n) for n = 0..482
- Lev Glebsky, Melany Licón, Luis Manuel Rivera, On the number of even roots of permutations, arXiv:1907.00548 [math.CO], 2019.
Crossrefs
Programs
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Maple
E:= (1/2)*exp(x + (1/2)*x^2 + (1/3)*x^3 + (1/4)*x^4 + (1/6)*x^6+(1/12)*x^(12)) - (1/2)*exp(x - (1/2)*x^2 + (1/3)*x^3 - (1/4)*x^4 - (1/6)*x^6-(1/12)*x^(12)): S:= series(E,x,31): seq(coeff(S,x,i)*i!,i=0..30); # Robert Israel, Jul 08 2019
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Mathematica
With[{nn = 22}, CoefficientList[Series[1/2 Exp[x + x^2/2 + x^3/3 + x^4/4 + x^6/6 +x^12/12]-1/2 Exp[x - x^2/2 + x^3/3 - x^4/4 - x^6/6 - x^12/12], {x, 0, nn}], x]*Range[0, nn]!]
Formula
E.g.f.: (1/2)*exp(x + (1/2)*x^2 + (1/3)*x^3 + (1/4)*x^4 + (1/6)*x^6+(1/12)*x^(12)) - (1/2)*exp(x - (1/2)*x^2 + (1/3)*x^3 - (1/4)*x^4 - (1/6)*x^6-(1/12)*x^(12)).