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A053505 Number of degree-n permutations of order dividing 30. 35
1, 1, 2, 6, 18, 90, 540, 3060, 20700, 145980, 1459800, 13854600, 140059800, 1514748600, 15869034000, 285268878000, 4109761962000, 59488383690000, 935767530036000, 13364309726748000, 240338216104020000, 4540941256642020000, 79739974380153240000 (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+1/5*x^5+1/6*x^6+1/10*x^10+1/15*x^15+1/30*x^30).

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, 5, 6, 10, 15, 30])))

    end:

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

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, 5, 6, 10, 15, 30}}]]]; Table[a[n], {n, 0, 25}] (* Jean-Fran├žois Alcover, Mar 03 2014, after Alois P. Heinz *)

CROSSREFS

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

Column k=30 of A008307.

Sequence in context: A273001 A118455 A165774 * A000138 A028857 A052687

Adjacent sequences:  A053502 A053503 A053504 * A053506 A053507 A053508

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 15 2000

STATUS

approved

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Last modified October 18 14:29 EDT 2018. Contains 316321 sequences. (Running on oeis4.)