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A308648 Number of degree-n odd permutations of order dividing 8. 0
0, 0, 1, 3, 12, 40, 120, 336, 7168, 58752, 345600, 1682560, 15983616, 142192128, 2318697472, 25614382080, 282753361920, 2645093410816, 48869743454208, 674729909839872, 12153962014842880, 167314499427532800, 1986101341059956736, 20335611320801886208 (list; graph; refs; listen; history; text; internal format)
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 A308654

KEYWORD

easy,nonn

AUTHOR

Luis Manuel Rivera Martínez, Jun 14 2019

STATUS

approved

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Last modified July 21 02:02 EDT 2019. Contains 325189 sequences. (Running on oeis4.)