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A053498 Number of degree-n permutations of order dividing 8. 2
1, 1, 2, 4, 16, 56, 256, 1072, 11264, 78976, 672256, 4653056, 49810432, 433429504, 4448608256, 39221579776, 607251736576, 7244686764032, 101611422797824, 1170362064019456, 19281174853615616, 261583327556386816, 4084459360167657472, 54366023748591386624 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.2.10.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..200

L. Moser and M. Wyman, On solutions of x^d = 1 in symmetric groups, Canad. J. Math., 7 (1955), 159-168.

FORMULA

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

MAPLE

a:= proc(n) option remember; `if`(n<0, 0, `if`(n=0, 1,

       add(mul(n-i, i=1..j-1)*a(n-j), j=[1, 2, 4, 8])))

    end:

seq(a(n), n=0..25);  # Alois P. Heinz, Feb 14 2013

MATHEMATICA

CoefficientList[Series[Exp[x+x^2/2+x^4/4+x^8/8], {x, 0, 23}], x]*Range[0, 23]! (* Jean-Fran├žois Alcover, Mar 24 2014 *)

CROSSREFS

Cf. A000085, A001470, A001472, A053495-A053505, A005388, A261428.

Column k=8 of A008307.

Sequence in context: A010362 A262164 A001472 * A005388 A053503 A153957

Adjacent sequences:  A053495 A053496 A053497 * A053499 A053500 A053501

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 15 2000

STATUS

approved

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Last modified February 24 12:51 EST 2018. Contains 299623 sequences. (Running on oeis4.)