A308648 - OEIS

%I #30 Jun 14 2019 19:26:31

%S 0,0,1,3,12,40,120,336,7168,58752,345600,1682560,15983616,142192128,

%T 2318697472,25614382080,282753361920,2645093410816,48869743454208,

%U 674729909839872,12153962014842880,167314499427532800,1986101341059956736,20335611320801886208

%N Number of degree-n odd permutations of order dividing 8.

%F 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).

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

%t With[{nn = 22},

%t 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]!]

%Y Cf. A061131, A061136, A061137.

%K easy,nonn

%O 0,4

%A _Luis Manuel Rivera Martínez_, Jun 14 2019