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A053501 Number of degree-n permutations of order dividing 11. 1
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3628801, 43545601, 283046401, 1320883201, 4953312001, 15850598401, 44910028801, 115482931201, 274271961601, 609493248001, 1279935820801, 4644633666390681601, 106826520356358566401, 1281918194457262387201 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,12

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

Vladimir Kruchinin, D. V. Kruchinin, Composita and their properties , arXiv:1103.2582 [math.CO], 2011-2013.

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+1/11*x^11).

a(n) = n!*sum(if mod(11*k-n,10)=0 then C(k,(11*k-n)/10)*(11)^((k-n)/10)/k! else 0; k=1..n), n>0. - Vladimir Kruchinin, Sep 10 2010

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, 11])))

    end:

seq(a(n), n=0..30);  # Alois P. Heinz, Feb 14 2013

MATHEMATICA

a[n_] := n!*Sum[If[Mod[11*k-n, 10] == 0, Binomial[k, (11*k-n)/10]*11^((k-n)/10)/k!, 0], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 24}] (* Jean-Fran├žois Alcover, Mar 20 2014, after Vladimir Kruchinin *)

PROG

(Maxima) a(n):=n!*sum(if mod(11*k-n, 10)=0 then binomial(k, (11*k-n)/10)*(11)^((k-n)/10)/k! else 0, k, 1, n); /* Vladimir Kruchinin, Sep 10 2010 */

CROSSREFS

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

Column k=11 of A008307.

Sequence in context: A071552 A181726 A195394 * A229677 A253992 A253999

Adjacent sequences:  A053498 A053499 A053500 * A053502 A053503 A053504

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 15 2000

STATUS

approved

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Last modified October 18 10:23 EDT 2018. Contains 316321 sequences. (Running on oeis4.)