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A053504 Number of degree-n permutations of order dividing 24. 2
1, 1, 2, 6, 24, 96, 576, 3312, 26496, 198144, 1691136, 14973696, 193370112, 2034809856, 25087186944, 313539434496, 4421478721536, 58307347556352, 915011420737536, 13553664911437824, 240637745416421376, 3965015057937924096 (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+1/3*x^3+1/4*x^4+1/6*x^6+1/8*x^8+1/12*x^12+1/24*x^24).

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, 3, 4, 6, 8, 12, 24])))

    end:

seq(a(n), n=0..25);  # Alois P. Heinz, Jan 25 2014

MATHEMATICA

a[n_] := a[n] = If[n<0, 0, If[n == 0, 1, Sum[Product[n-i, {i, 1, j-1}]*a[n-j], {j, {1, 2, 3, 4, 6, 8, 12, 24}}]]]; Table[a[n], {n, 0, 25}] (* Jean-Fran├žois Alcover, Mar 19 2014, after Alois P. Heinz *)

With[{nn=30}, CoefficientList[Series[Exp[Total[x^#/#&/@Divisors[24]]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Mar 05 2016 *)

PROG

(PARI) N=22; x='x+O('x^N);

Vec(serlaplace(exp(sumdiv(24, d, x^d/d)))) \\ Gheorghe Coserea, May 11 2017

CROSSREFS

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

Column k=24 of A008307.

Sequence in context: A152324 A147887 A053502 * A215716 A060725 A150299

Adjacent sequences:  A053501 A053502 A053503 * A053505 A053506 A053507

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 15 2000

STATUS

approved

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Last modified October 20 07:17 EDT 2018. Contains 316378 sequences. (Running on oeis4.)