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A053500 Number of degree-n permutations of order dividing 10. 1
1, 1, 2, 4, 10, 50, 220, 1240, 6140, 32860, 602200, 5668400, 62030200, 522328600, 4487190800, 62591332000, 715163146000, 9573774122000, 105731659828000, 1187355279592000, 29205778751300000, 481597207656340000, 9086318388933400000, 132525988426667120000 (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+1/5*x^5+1/10*x^10).

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, 5, 10])))

    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, 5, 10}}]]]; 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=10 of A008307.

Sequence in context: A113208 A173488 A000613 * A214724 A080090 A125263

Adjacent sequences:  A053497 A053498 A053499 * A053501 A053502 A053503

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 15 2000

STATUS

approved

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Last modified February 24 18:24 EST 2018. Contains 299628 sequences. (Running on oeis4.)