A308648 Number of degree-n odd permutations of order dividing 8.

0, 0, 1, 3, 12, 40, 120, 336, 7168, 58752, 345600, 1682560, 15983616, 142192128, 2318697472, 25614382080, 282753361920, 2645093410816, 48869743454208, 674729909839872, 12153962014842880, 167314499427532800, 1986101341059956736, 20335611320801886208

Offset: 0

Author

Luis Manuel Rivera Martínez, Jun 14 2019

Keywords

• easy
• nonn

Examples

			For n=3 the a(3)=3 solutions are (1, 2), (1, 3), (2, 3) (permutations in cyclic notation).
		

Crossrefs

Cf. A061131, A061136, A061137.

Programs

Mathematica

With[{nn = 22},
CoefficientList[Series[1/2 Exp[x + x^2/2 + x^4/4 + x^8/8] - 1/2 Exp[x - x^2/2 - x^4/4 - x^8/8], {x, 0, nn}], x]*Range[0, nn]!]

Formula

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