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

0,4

Links

Table of n, a(n) for n=0..23.

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).

Example

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

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]!]

Crossrefs

Cf. A061131, A061136, A061137.

Sequence in context: A080929 A052482 A061136 * A247002 A027991 A120304

Adjacent sequences: A308645 A308646 A308647 * A308649 A308650 A308651

Keyword

easy,nonn

Author

Luis Manuel Rivera Martínez, Jun 14 2019

Status

approved