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A053501 Number of degree-n permutations of order dividing 11. 3
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
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 + x^11/11).
a(n) = n!*Sum_{k=1..n} (if mod(11*k-n,10)=0 then C(k,(11*k-n)/10)*(11)^((k-n)/10)/k!, else 0), 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-François Alcover, Mar 20 2014, after Vladimir Kruchinin *)
With[{m = 30}, CoefficientList[Series[Exp[x +x^11/11], {x, 0, m}], x]*Range[0, m]!] (* G. C. Greubel, May 15 2019 *)
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 */
(PARI) my(x='x+O('x^30)); Vec(serlaplace( exp(x +x^11/11) )) \\ G. C. Greubel, May 15 2019
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(x + x^11/11) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, May 15 2019
(Sage) m = 30; T = taylor(exp(x +x^11/11), x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # G. C. Greubel, May 15 2019
CROSSREFS
Column k=11 of A008307.
Sequence in context: A071552 A181726 A195394 * A229677 A350335 A253992
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 15 2000
STATUS
approved

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Last modified May 23 18:13 EDT 2024. Contains 372765 sequences. (Running on oeis4.)