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A053499
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Number of degree-n permutations of order dividing 9.
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5
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1, 1, 1, 3, 9, 21, 81, 351, 1233, 46089, 434241, 2359611, 27387801, 264333213, 1722161169, 16514298711, 163094452641, 1216239520401, 50883607918593, 866931703203699, 8473720481213481, 166915156382509221, 2699805625227141201, 28818706120636531023, 439756550972215638129, 6766483260087819272601, 77096822666547068590401, 3568144263578808757678251
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OFFSET
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0,4
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COMMENTS
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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^3/3 + x^9/9).
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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, 3, 9])))
end:
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MATHEMATICA
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CoefficientList[Series[Exp[x+x^3/3+x^9/9], {x, 0, 30}], x]*Range[0, 30]! (* Jean-François Alcover, Mar 24 2014 *)
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PROG
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(PARI) my(x='x+O('x^30)); Vec(serlaplace( exp(x + x^3/3 + x^9/9) )) \\ G. C. Greubel, May 15 2019
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(x + x^3/3 + x^9/9) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, May 15 2019
(Sage) m = 30; T = taylor(exp(x + x^3/3 + x^9/9), 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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