

A290095


a(n) = A275725(A060126(n)); prime factorization encodings of cyclepolynomials computed for finite permutations listed in reversed colexicographic ordering.


8



2, 4, 18, 8, 8, 12, 150, 100, 54, 16, 16, 24, 54, 16, 90, 40, 36, 16, 16, 24, 40, 60, 16, 36, 1470, 980, 882, 392, 392, 588, 750, 500, 162, 32, 32, 48, 162, 32, 270, 80, 108, 32, 32, 48, 80, 120, 32, 72, 750, 500, 162, 32, 32, 48, 1050, 700, 378, 112, 112, 168, 450, 200, 162, 32, 32, 72, 200, 300, 32, 48, 108, 32, 162, 32, 270, 80, 108, 32, 378, 112, 630, 280
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OFFSET

0,1


COMMENTS

In this context "cyclepolynomials" are singlevariable polynomials where the coefficients (encoded with the exponents of prime factorization of n) are equal to the lengths of cycles in the permutation listed with index n in table A055089 (A195663). See the examples.


LINKS

Antti Karttunen, Table of n, a(n) for n = 0..40319
Index entries for sequences related to factorial base representation


FORMULA

a(n) = A275725(A060126(n)).
Other identities:
A046523(a(n)) = A290096(n).
A056170(a(n)) = A055090(n).
A046660(a(n)) = A055091(n).
A072411(a(n)) = A055092(n).
A275812(a(n)) = A055093(n).


EXAMPLE

Consider the first eight permutations (indices 07) listed in A055089:
1 [Only the first 1cycle explicitly listed thus a(0) = 2^1 = 2]
2,1 [One transposition (2cycle) in beginning, thus a(1) = 2^2 = 4]
1,3,2 [One fixed element in beginning, then transposition, thus a(2) = 2^1 * 3^2 = 18]
3,1,2 [One 3cycle, thus a(3) = 2^3 = 8]
2,3,1 [One 3cycle, thus a(4) = 2^3 = 8]
3,2,1 [One transposition jumping over a fixed element, a(5) = 2^2 * 3^1 = 12]
1,2,4,3 [Two 1cycles, then a 2cycle, thus a(6) = 2^1 * 3^1 * 5^2 = 150].
2,1,4,3 [Two 2cycles, not crossed, thus a(7) = 2^2 * 5^2 = 100].


CROSSREFS

Cf. A055090, A055091, A055092, A055093, A060126, A290096, A290097.
Cf. also A275725, A275734, A275735, A276076 and tables A055089, A195663.
Sequence in context: A136147 A275837 A119510 * A275725 A242528 A137933
Adjacent sequences: A290092 A290093 A290094 * A290096 A290097 A290098


KEYWORD

nonn


AUTHOR

Antti Karttunen, Aug 17 2017


STATUS

approved



