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A053501
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Number of degree-n permutations of order dividing 11.
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3
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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
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OFFSET
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0,12
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REFERENCES
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R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.2.10.
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LINKS
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FORMULA
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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
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MAPLE
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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:
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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