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A053499 Number of degree-n permutations of order dividing 9. 3
1, 1, 1, 3, 9, 21, 81, 351, 1233, 46089, 434241, 2359611, 27387801, 264333213, 1722161169, 16514298711, 163094452641, 1216239520401, 50883607918593, 866931703203699, 8473720481213481, 166915156382509221, 2699805625227141201, 28818706120636531023, 439756550972215638129, 6766483260087819272601, 77096822666547068590401, 3568144263578808757678251 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Differs from A218003 first at n=27. - Alois P. Heinz, Jan 25 2014

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+1/3*x^3+1/9*x^9).

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, 3, 9])))

    end:

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

MATHEMATICA

CoefficientList[Series[Exp[x+x^3/3+x^9/9], {x, 0, 23}], x]*Range[0, 23]! (* Jean-Fran├žois Alcover, Mar 24 2014 *)

CROSSREFS

Cf. A000085, A001470, A001472, A053495-A053505, A005388, A261429.

Column k=9 of A008307.

Sequence in context: A236856 A001470 A118932 * A218003 A146909 A146248

Adjacent sequences:  A053496 A053497 A053498 * A053500 A053501 A053502

KEYWORD

nonn,changed

AUTHOR

N. J. A. Sloane, Jan 15 2000

STATUS

approved

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Last modified June 18 07:40 EDT 2018. Contains 305542 sequences. (Running on oeis4.)