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A053502 Number of degree-n permutations of order dividing 12. 1
1, 1, 2, 6, 24, 96, 576, 3312, 21456, 152784, 1237536, 9984096, 133494912, 1412107776, 16369357824, 206123325696, 2866280276736, 36809077162752, 592066290710016, 8800038127378944, 136876273991755776, 2197453620220010496, 37915306084793106432 (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+1/12*x^12).

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, 12])))

    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, 4, 6, 12}}]]]; Table[a[n], {n, 0, 25}] (* Jean-Fran├žois Alcover, Apr 24 2014, after Alois P. Heinz *)

CROSSREFS

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

Column k=12 of A008307.

Sequence in context: A152331 A152324 A147887 * A053504 A215716 A060725

Adjacent sequences:  A053499 A053500 A053501 * A053503 A053504 A053505

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 15 2000

STATUS

approved

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Last modified November 18 17:49 EST 2018. Contains 317323 sequences. (Running on oeis4.)