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Search: id:A074064
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| A074064 |
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Number of cycle types of degree-n permutations having the maximum possible order. |
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3
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| 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 1, 1, 1, 1, 2, 3, 1
(list; graph; listen)
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OFFSET
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1,6
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FORMULA
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Coefficient of x^n in expansion of Sum_{i divides A000793(n)} mu(A000793(n)/i)*1/Product_{j divides i} (1-x^j).
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EXAMPLE
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For n = 22 we have 4 such cycle types: [1, 1, 1, 3, 4, 5, 7], [1, 2, 3, 4, 5, 7], [3, 3, 4, 5, 7], [4, 5, 6, 7].
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MAPLE
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A000793 := proc(n) option remember; local l, p, i ; l := 1: p := combinat[partition](n): for i from 1 to combinat[numbpart](n) do if ilcm( p[i][j] $ j=1..nops(p[i])) > l then l := ilcm( p[i][j] $ j=1..nops(p[i])) ; fi: od: RETURN(l) ; end: taylInv := proc(i, n) local resul, j, idiv, k ; resul := 1 ; idiv := numtheory[divisors](i) ; for k from 1 to nops(idiv) do j := op(k, idiv) ; resul := resul*taylor(1/(1-x^j), x=0, n+1) ; resul := convert(taylor(resul, x=0, n+1), polynom) ; od ; coeftayl(resul, x=0, n) ; end: A074064 := proc(n) local resul, a793, dvs, i, k ; resul := 0: a793 := A000793(n) ; dvs := numtheory[divisors](a793) ; for k from 1 to nops(dvs) do i := op(k, dvs) ; resul := resul+numtheory[mobius](a793/i)*taylInv(i, n) ; od : RETURN(resul) ; end: for n from 1 to 80 do print(n, A074064(n)) ; od; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 30 2007
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CROSSREFS
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Cf. A000793, A074859.
Sequence in context: A106752 A136441 A030561 this_sequence A139549 A130782 A055457
Adjacent sequences: A074061 A074062 A074063 this_sequence A074065 A074066 A074067
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KEYWORD
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easy,more,nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)Eunet.yu), Sep 15 2002
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 30 2007
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